A patronymic is a surname formed from the name of the owner's father or a paternal ancestor, used by a culture in place of a family name that is handed down from generation to generation. As an interesting note, while some cultures exist that do use matronymics (names derived from one's mother), more often in a culture that uses patronymics, taking such a name is a sign of illegitimacy.
One of the cultures that used matronymics in the old days without it being an obvious sign of illegitimacy was the English culture. It was traditional for posthumous children in medieval times to take their mother's name as a surname, and kids faced with a sucky patronym and a cool matronym were free to choose the latter. Custer, Beaton, Izzard, Madison, and Parnell are only a few of the many matronyms used in English as surnames.
There are only a few cultures on modern Earth that still retain the use of a patronymic (Eastern Europe, Russia, Mongolia, Iceland, Malaysia, and Arabic countries); it just gets awkward as the populations get high, so most of these cultures (with the notable exception of Iceland, which does not have surnames bar a select few families that have had them since before taking up family names was forbidden by law) cheat by adopting proper surnames or other monikers as well. Not so for alien species in Science Fiction. Most alien races have Only One Name, and among those who don't, it's usually a patronymic. Especially proud warrior races.
Less often, but still more common than a proper surname, a character will use a locative name (Such as Xev of B3K from Lexx). Various Jaffa in Stargate SG-1 have used either (and the cultural bias is demonstrated by Master Bra'tac, who always referred to General Hammond as "Hammond of Texas"). The proudest of the warrior races have both.
Taken to extremes, can easily form the basis for an Overly Long Name.
See also I Am X, Son of Y
Kamichama Karin gives us Kazune and Kazusa, children of Kujyou Kazuto, as well as Kirika and Kirio, children of Kirihiko Karasuma. And Suzune's name takes a kanji each from both Karin and Kazune's names.
In DC Comics, Thanagarians have males take their given name from their father's surname (Katar Hol's father was Paran Katar), while females take their surname from their father's given name (Shayera Thal's father was Thal Porvis). There have been variations, usually by writer's who don't know the rules.
Likewise, Kryptonian males are given a name which is attached to their surname, as in Kal-El (Kal of the House of El). Kryptonian females have a given name attached to a patronymic in the form of their father's name, as in Kara Zor-El (Kara, daughter of Zor, of the House of El). There are variants, as with Cir-El (who was not technically Kryptonian anyway) but those can generally be ascribed to Clark valuing human norms over Kryptonian ones.
Thorgal: justified by the viking background. Thorgal Aegirsson (Messenger of Thor, son of Aegir), Aaricia Gandalfdottir, Jolan Thorgalson, Louve Thorgaldottir, Aniel Thorgalson...
Some Gauls in Astérix, although mostly for humour value. Semiautomatix -> Fulliautomatix, Astronomix -> Asterix, Obeliscoidix -> Obelix. There's also the historical example of Caesar -> Caesarion.
The Drac in the movie Enemy Mine are parthenogenetic (meaning each child only has one parent.) Each Drac has a first and last name, plus a long list of ancestors names which they must remember and recite at a coming of age ceremony. (Davidge, a human character who adopted a Drac as his son, gets his own name added to the boy's lineage.)
Weird subversion: Thanks to a miscommunication, the Arab protagonist of The 13th Warrior became known as "Eben" — a mispronunciation of the Arabic word "ibn", which means "son of".
Herger the Joyous: (to Ahmed) "Quis est vestri nomen?"
Melchisidek: (translating) "He wants to know your name."
Ahmed ibn Fahdlan: "My name is Ahmed ibn Fahdlan ibn al-Abbas ibn Rashid ibn Hamad."
Herger the Joyous: "Eben?"
Ahmed ibn Fahdlan: "No, listen, My name is Ahmed Ibn Fahdlan. "Ibn" means "son of"."
In J. R. R. Tolkien's Legendarium/Middle-earth world (The Lord of the Rings, etc) most peoples make use of patronymics. The only ones to use modern-style family names are the Shire-Hobbits, and the Men and Hobbits of Bree-land (both lands which are culturally closest to modern day). Thus, for example, the dwarf Thorin Oakenshield (the latter name is an epithet, an earned one) is Thorin, son of Thráin, son of Thrór, while hobbit Frodo Baggins introduced himself as "Frodo, son of Drogo" when abroad.
Parodied in Discworld, where Dwarves often get uncreative. An example can be Snorriscousin or Glodsnephew. Also their patronymic surnames can stack, leading to Glodsonsonsonsonsonsonsons...
The Culture in Iain M. Banks's sci-fi novels have a complicated naming system, which is more a potted biography - it includes at least one name given by the parents, one family name, one name based on the place they were born, one name based on their place of residence, and one name chosen by the people themselves when they reach maturity. As an example, the Author would be "Sol-Terrasa Iain El-Bonko Banks da'NorthQueensferry". He's occasionally actually used the Anglicised version.
In Tamora Pierce's The Immortals, the people of the country of Galla use patronymics, a fact that is important in the history of Veralidaine Sarrasri (aka Daine) because, as a Heroic Bastard, she must use her mother's name as a matronymic, which draws scrutiny to her and her status as a bastard.
The Seventh Tower has the Chosen hyphenate their parents' names (e.g., "Tal Graile-Rerem"), while the Icecarls have been known to introduce themselves with several generations of their ancestry (e.g., "I am Milla, daughter of Ylse, daughter of Emor, daughter of Rohen, daughter of Cylo, in the line of Danir since the Ruin of the Ship"). Not only that, Icecarls also can earn Oakenshield-style epithets.
Members of the House of the Dragon in the Dragaera series use a patronymic of an extremely illustrious ancestor, which is unique to that House; members of other houses just use their given name and title.
In Lloyd Alexander's Chronicles of Prydain, the pattern is slightly different. Male characters go by the patronymic, but females use a matronymic. Thus, the Prince of Mona was Rhun son of Rhuddlum, but his mother was Teleria daughter of Tannwen. Eilonwy tended to be referenced by the very lengthy name The Princess Eilonwy daughter of Angharad daughter of Regat of the House of Llyr.
And that would have gone even longer had Eilonwy been able to remember the names of any of Regat's female ancestors.
The science fiction novel Cagebird has a protagonist from an apparently rather traditional Russian family. He uses a patronymic as his middle name until he's recruited by Space Pirates, although it's only mentioned once or twice.
Wild Cards' Dr. Tachyon has a Takisian name that lists his entire geneology for a thousand generations.
Robert Jordan's Wheel of Time series has the Ogier, whose males introduce themselves with a double patronymic (Loial son of Arent son of Halan), and whose females introduce themselves with a double matronymic (Erith daughter of Ila daughter of Alar).
Modified in David Brin's Uplift series. Each sentient species is "uplifted" from pre-sentience by a patron species. When a person is formally introduced, he identifies his species with all its patronymics—the names of all the patron species that are not yet extinct. (As in, "Bubbacub, a-Pil, ab-Kisa-ab-Soro-ab-Hul-ab-Puber-ul-Gello-ul-Pring".note "Bubbacub, of the species Pil, who were uplifted by the Kisa, who were uplifted by the Soro, who were uplifted by the Hul, who were uplifted by the Puber (the Puber's patrons now being extinct); the Pila having themselves uplifted the Gello and the Pring" Even with the abbreviated prefixes, introductions can take a while.)
Humans have no known patron race so human characters are introduced as "a-Human, ul-Dolphin-ul-Chimp" and a neo-dolphin or chimpanzee would be "ab-Human". Because of that most of Galactic society treats us as orphan bastards.
The Shin culture in The Stormlight Archive use patronymics so you get names like Shauka-daughter-Haswerth and Thresh-son-Esan, Szeth-son-son-Vallano is an exile and outcast and uses his grandfather's name because he doesn't want to dishonour his father.
In The Gospels, Jesus's enemies are shown referring to him as "Mary's son", thus calling attention to the uncertainty on his father's identity.
Many Biblical figures have patronymic names. One that has Hilarious in Hindsight connotations today is "Joshua, Son of Nun".
Bartholomew is an apostle of Jesus mentioned in three of the four Gospels. His name is an Anglicized form of Greek Bartholomaios, which would be Bar Tolmai, "son of Tolmai", in Aramaic. It's usually accepted that Bartholomew is the same as "Nathanael" from the Gospel of John, which doesn't mention the name "Bartholomew".
The apostle Simon Peter is called "Simon son of Jonah" in the Gospel of Matthew and "Simon son of John" in the Gospel of John.
A blind man Jesus heals is called Bartimaeus in Latin or Bartimaios in Greek, meaning "son of Timai" in Aramaic.
Barabbas, the man spared from death instead of Jesus, has a name meaning "son of the father". Some manuscripts even give Barabbas's full name as "Jesus Barabbas" - not unlikely, as Jesus (or rather the name later rendered as Jesus, Yeshua) was a common Jewish name.
A popular naming convention in S.M. Stirling's Emberverse, with characters known as "Jake sunna Jake" (say it aloud and it makes perfect sense), Dik Tomskid, Bjarni Erickson, and Asgerd Karlsdottir.
On Marion Zimmer Bradley's Darkover, a woman who joins the Renunciates (aka the "Free Amazons") takes an oath in which, among other things, she agrees not to use the name of her father or her husband. She is thereafter known by her matronymic, e.g., "Margali n'ha [daughter of] Ysabet."
Animorphs has two examples. Andalite parents pass down their middle names to their children. Ax's middle name, Esgarrouth, was from his father's middle name, and Elfangor's middle name, Sirinal, was from his mother's middle name. Usually the problem of too many children didn't come into play as they had a one child per family policy until some were allowed a second child. Yeerks, meanwhile, are designated by their parent grub. So, Edriss 562, Visser One, would be the 562nd grub of the Edriss tri-parent.
The world of Diane Duane's The Tale of the Five uses patronymics and matronymics depending on the gender of the child; a son is s'[Father's name], and a daughter is d'[Mother's name].
Characters in The Granite Shield use Welsh patronymics and matronymics, depending on gender but subverted on occasion due to Gender Is No Object. The protagonists' mother is Llewellynne ap Rowena; one of her sons is named Llewen ap Tuedwur after his legitimate father but the other is a Royal Bastard named Rhys ap Llewellynne ap Owain after his mother and maternal grandfather.
Barrayar has this for the Vor lords. First sons of Counts are given their paternal grandfather's first name as their first name, while their maternal grandfather's first name becomes their second name (For example: Count Piotr Pierre Vorkosigan). Miles would have originally been Piotr Miles Vorkosigan, but after he was born deformed, his mother gave him her father's full name: Miles Naismith Vorkosigan. Second sons are given the second names of their grandfather (Like Mark Pierre Vorkosigan).
Live Action TV
The Nietzscheans of Andromeda: They had a surname, a clan name and both a patronymic and a matronymic. One character's full name was "Tyr Anasazi of Kodiak Pride out of Victoria by Barbarossa".
Not so much a patronymic as a short genealogy. Tyr is also at one point asked which Barbarossa was his father. Justified because Nietzscheans breed towards very specific traits, and knowing enough of your ancestry to avoid inbreeding is not a bad thing.
In Star Trek, Klingons, if they're forced to give more than one name, give a patronymic (Worf, son of Mogh). They will also on occasion refer to their House. (For complicated political reasons, Worf is affiliated with General Martok's House, due to his own House being disbanded in disgrace for the good of the Empire). Vulcans use these as well in religious ceremonies, and give two names (the second is presumed to be the name of the paternal grandfather). It's worth noting that Vulcans do have family names, but they're unpronounceable by humans.
Interestingly, Worf's son Alexander, when joining the Imperial Defense Force, uses his human name Alexander Rozhenko, with "Rozhenko" being the surname of Worf's foster parents. Nobody bats an eyelash at this strange, for a Klingon, name, although Martok does ask him what house he represents. Alexander claims he is of no house, and this satisfies Martok.
In Norse Mythology, Thor is sometimes called "Óðinsson", which is just the way the Norse ran things in those days. The famous Viking explorer Leifr Eiríksson was, in fact, the son of Eiríkr the Red.
Loki also had a rare matronym with "Laufeyjarson".
According to the 3rd Edition Forgotten Realms Campaign Setting, humans from Unther tend to use patronymics, whereas most other cultures prefer surnames.
Anyone who addresses Dante of Devil May Cry as "Son of Sparda" usually has malicious, or at least not-so-nice, intent.
In WarCraft, Thrall, leader of the Horde as of the third game (and World of Warcraft), is known as the "Son of Durotan", who was known to all as the late chief of the Frostwolf clan.
Strangely, very few orcs introduce themselves this way. Mostly, they just go with a single name. If they have a nickname (usually passed down from father to son like "Doomhammer", "Hellscream", or "Blackhand"), it will be added.
Orc lastnames in The Elder Scrolls are "gro" (masculine) or "gra" (feminine) apparently meaning "son of" or "daughter of" respectively.
Nords will do this sometimes as well, being heavily based on early Scandinavian culture. For example, Archmage Gauldur's three sons all had the surname "Gauldurson".
The robotic characters in Primordia take on "fabrinymics" in honor of whoever created them. For example, Horatio's friend/helper/sidekick Crispin was built by Horatio, and thus is formally named "Crispin Horatiobuilt". Early robots that were created by humans before the mankind went extinct have the common fabrinymic "Manbuilt". Horatio refers to himself as "Horatio Nullbuilt", because he doesn't remember his origins due to unreadable files in his memory. He eventually turns out to be a backup of the AI of the ship he and Crispin live in - his real name is "HORUS Manbuilt".
Fabrinymics can also "stack" in a variety of ways, tracing several generations of machines. At one point, Horatio has to resolve a dispute between two brothers, Oswald and Cornelius Factorbuilt, regarding a small robot Rex they created together. The best possible solution is to notice that none of the brothers could have built that robot alone - but because they share the same fabrinymic, they can call Rex "Factorbuiltbuilt", thus gaining equal "buildership" over him.
In the web original My Friend is an Alien, a series of stories about a group of kids who befriend two aliens, the aliens have a quadruple patronymic (Jahv and Keyro, sons of Amshat, son of Lemoy, son of Dekel, son of Gershon).
The ancient Romans often didn't bother naming daughters, so instead of names they'd get first, second, third (as in "third daughter"). The end result of this was most women could only really be named with a patronymic name, or it'd be impossible to tell them apart. They were only slightly less lazy when naming sons, and tended to number them, too.
It wasn't so bad as all that; daughters would have variations on their father's clan name. The confusing part is that aristocratic fathers would often name their eldest sons after themselves with no numbers, leading to generation after generation of guys named Publius Claudius Pulcher. Only slightly better than Planet of Steves.
Girls mostly got the feminine version of their father's family name - Marc Antony's daughter was named Antonia and Augustus' daughter was Julia, for example. They did sometimes get nicknames - sometimes as simple as Maior and Minor and sometimes more creative - to tell them apart. A lot of the time, though, you just had to learn to keep all your Cornelias straight.
Roman nicknames, known as "cognomen", were actually a formally recognized parts of a person's full name — mostly because Romans really were rather unimaginative with given names (called "praenomen" in Latin, the Romans had about three dozen different praenomens in total, out of which only a dozen are regularly used), and even one clan could have a lot of the similarly named guys. What's interesting is that in the late Republic cognomens also became hereditary and turned into an ersatz-family name, to distinguish the branches in The Clan. This, in turn caused an another round of nicknaming, this time called "agnomen" — for example Caligula's full name was Gaiusnote praenomen or given name Juliusnote nomen gentile, family name proper Caesarnote originally Caesar's cognomen, but it was adopted by all subsequent Roman Emperors as a title Germanicusnote cognomen, or nickname, meaning "the conqueror of Germany". Caligula actually inherited it from his father, who was called exactly the same except for the "Caligula" bit and is generally known simply as Germanicus Caligulanote agnomen, or second nickname, meaning "a Little Boot", after heavy military sandals worn by legionnaires. Caligula, being a Military Brat, wore a smaller version of them in his childhood, and was nicknamed thusly..
More in line with proper patronymics, the full name listed on official records would often include a filiation, which basically inserted the praenomina of his father and grandfather between the nomen and the cognomen. The Gaius Julius Caesar that everyone knows and loves would have been listed as "Gaius Iulius Gaii filiusnote "son of Gaius" Gaii neposnote "grandson of Gaius" Caesar" (remember how we mentioned that the Romans got a bit uncreative with their names?), or "C. Iulius C. f. C. n. Caesar" for short.
Ancient Greece did this, Homer had the Atreides, i.e. Agamemnon and Menelaus.
Also with the Dioscuri (Scion of Zeus), Castor and Polydeuces - kind of a misnomer since only one was the son of Zeus. I guess they were just that inseparable.
Inversion: In Arabic culture, a Kunya is a nickname given to a person referring to their first-born child or son in the form of Abu (=father of) [child's name] for fathers and Umm (=mother of) [child's name] for mothers. The rule is that if the eldest child is a daughter, the Kunya will refer to her until a younger brother is born, at which point the parents customarily adopt a new Kunya from the son's name; thus if a man first had a daughter named Fatima in 1990 a son named Ahmed in 1995, he would be "Abu Fatima" 1990-1995 and then "Abu Ahmed" 1995 onwards. If the child dies, however, the Kunya remains the same; for example, Palestinian president Mahmoud Abbas is still known as Abu Mazen (father of Mazen), even though Mazen died in 2002.
However, Arabic names also tend to have patronymics as well. The structure of an Arabic name is: Kunya (Abu/Umm, Father of/Mother of), Ism (a person's given name), Laqab (a nickname or description of the person or their character; this can be heritable, rather like a Roman cognomen), Nasab (the patronymic often two generations back, given with ibn/bint son of/daughter of), and Nisba (like a surname. Usually a family name, area or tribe of origin, or occupation). Ex. Abu Kareem Muhammad al-Jameel ibn Nidh'aal ibn Abdulazeez al-Filisteeni would mean "Father of Kareem, Muhammad the beautiful, son of Nidh'all, son of Abdulazeez, the Palestinian."
In many modern Arabic speaking countries, only the patronymics have legal significance, and the "Ibn" or "Bint" part is usually left out. In historical times, there was a great deal of variation as to the order of the various names too, with only the personal name and the patronymics being in a set order.
For clarity: Arabs in the eastern part of the Arab world often use the name of their male-line great-grandfather (their father's father's father); this is known as an ism ruba`i ("fourth-name", more or less), since the middle two generations are often listed (e.g., Muhammad bin Adil bin Marwan bin Radwan, who would go as "Muhammad bin Radwan" for short, even though he's actually Adil's son).
In most Arab countries, however, the "bin" is dropped, so our example fellow in, say Egypt, would be called "Muhammad Adil Marwan Radwan" in official contexts (e.g. on his national ID card) and "Muhammad Radwan" elsewhere—unless he elects to go by "Muhammad Marwan," since it's common for people to use the grandfather's name (ism thalathi, or "third-name") as the "surname"; it varies depending on family.note For instance, one might go by his ruba`i name, but a friend of said person might go by his thalathi for the excellent reason that he would otherwise be "Muhammad Muhammad" (as, for that matter, would be like a fifth of all Egyptian men if people didn't have this option thanks to two Egyptian peculiarities—"Muhammad" being the most popular name in the country, and the tradition of naming your eldest son after your father).
The spread of bureaucracy in the Arab world in the 20th century has led to surnames being more or less cemented, so some use the forename of a relatively distant ancestor as a surname and pass that on to their children even though that would not normally be included in the nasab. This is usually done by picking out an ancestor with a name no longer in use by the family or society in general. For example, a guy named Ahmed whose father's name is Muhammad, grandfather was Ahmed, and great-grandfather was Hashim, his full ruba`i name would be "Ahmed Muhammad Ahmed Hashim", and would probably go by Ahmed Hashim. When he inevitably named his eldest son after his father, that child would be known as "Muhammad Hashim" and his official ruba`i name would be "Muhammad Ahmed Muhammad Hashim"—despite the fact that "Hashim" is actually five generations back, not four.
Some Arabs choose to use their nisba or laqab as a surname-equivalent instead (the al-Barghoutis/Barghouthis/etc. of Palestine notably use the nisba, while the famous Syrian-Egyptian musician Fareed al-Atrash used the laqab—it means "the Deaf"). This practice is most common in the Arab Maghreb (Morocco, Algeria, Tunisia, and Libya), where the laqab is very often "Bou[whatever]" (the Maghrebi way of saying "Abu[whatever]", i.e. "father of [whatever]" or metaphorically "the guy with the [whatever]"). Again, the nasab is used as a set of middle names.
A few Hebrew names used to work this way.
In The Bible, although it wasn't exactly part of the name, Hebrews would identify themselves by tribe.
"Traditional" Hebrew names are patronyms. They are still used for calling people to read from the Torah. Converts will use "Ben-Avraham", meaning "son of Abraham" (or "Bat-Avraham" meaning "daughter of Abraham), to connect them to their new people.
It's not just patronymic, but matronymic as well. For example, "Reuven ben Yaakov v'Leah" is Reuben, son of Jacob and Leah. And the traditional styling for a convert is usually "<name> ben/bat Avraham Aveinu v'Sarah Imeinu", or <name>, son/daughter of Abraham our father and Sarah our mother.
Ben or bat is not just a name for converts, though it does tend to appear mostly within the gap between Orthodox Jews (who have their own naming traditions) and the totally secular. For example, someone discussing Left Behind pointed to the name "Tzion Ben-Yehuda" as unrealistically Jewish. Oh really?
The person on the Left Behind page was talking about the mixed spelling. The use of tz, as is used when translitterating Hebrew, and the use of J, which doesn't exist in the Hebrew language. The point was just to be consistent.
Actually, the particular Hebrew letter can be transliterated as either J or Y.
Also, only the mother's name is used for some one who is sick. So when praying for someone who is ill you would call them for example Yoseph ben Shifra, rather than Yoseph ben Avraham v'Shifra.
Though no longer used as true patronymics, several surnames are patronymic in origin:
Those patronymic-style surnames of Germanic origin (English, German, Dutch, Scandinavia) have endings with "-son/-sen/-sohn". Iceland, which also belongs in this language group, still has proper patronymics.
In German patronymic-style surnames also include those that begin with a masculine given name and end in an "-s" (originally a genitive), "-i" or "-y" (originally a Latin genitive, from the fashion for Latinized names during the late middle ages and renaissance) or that are identical to a first name. Thus in German you can encounter "Jacobsen", "Jacobsohn", "Jacobs", "Jacobi", "Jacoby" and "Jacob" as surnames.
Irish and Scottish surnames, though no longer patronymic, have patronymic origins. McCarthy and O'Connor literally mean "son of Carthach" and "male descendant of Conchobar (or Connor in the modern era)", respectively.
This goes further in the Irish and Scottish languages, as these languages still treat surnames much like other examples of full patronymics. To take the Irish language examples from above (Mac Cárthaigh and Ó Conchobhair, respectively), we see two other forms used for women: Nic Chárthaigh (daughter of Carthach) and Ni Chonchobhair (female descendant of Conchobar), and Mhic Chárthaigh (wife of the son of Carthach) and Ui Chonchobhair (wife of the male descendant of Conchobar).
Many of the most common Spanish surnames ending in -ez are patronymics: Sánchez = "Son of Sancho", López = "Son of Lope", Rodríguez = "Son of Rodrigo", and so on. (counterexamples: Latin American names Chávez and Cortez are exceptions to this rule and come from Spanish surnames Chaves and Cortés, which in turn are derived from words for "Keys" and "Polite.")
Most Russian surnames are essentially archaic form of patronymics: "-ov" was a standard patronymic ending for commoners, while modern form "-vich" was used by nobility. Surnames ending on "-vich" are also common but less so and more in Western parts of the country.
Ukrainian also has its own similar suffices.
The same is true of the Balkan "-ić" ending, found in Croatian, Serbian, etc. names e.g.: Petrović, Jovanović
The ending "-vich" or "-ov" (and varieties thereof), generally speaking, denotes the form of a patronymic in Slavic languages. Some (e.g. Serbian and Croatian) seem to feature names ending in "-vich" (alternatively spelled "-vic") more commonly, while others (e.g. Russian and Bulgarian) seem to feature names ending in "-ov" more commonly.
In Iceland, this is even today Truth in Television to the point that taking a continental- or Anglophone-style family name is forbidden by law. The only people with family names are immigrants and their descendants (like former Prime Minister Geir Haarde, whose father was Norwegian).
Icelandic names are at least easy for an English speaker to parse. You can be sure that if you meet someone named Sif Ólafsdóttir that she is in fact, Sif, Ólaf's daughter.
This has the effect of rendering the concept of a family name—one passed from generation to generation—meaningless. The children of Eiríkur Ólafson could be Jón Eiríksson and Guðrún Eiríksdóttir, and Jón's children could then be Jónsson and Jónsdóttir. Unless they were named with a matronymic. Meaning that if you are looking up a friend in an Icelandic phonebook (which is organized by first names), you had better know the name of his or her father and/or mother.
Women do not take their husband's names on marriage, which leads to problems when travelling overseas, as many cultures do not permit unmarried couples to share hotel rooms and the difference in "last names" seems to indicate such status. Add in kids with seemingly different "last names" from their folks' names, and you get a real mess.
Matronyms are also used in Iceland, although they are nowhere nearly as common as patronyms. Unlike the trope description details there is no stigma attached, although a person may switch from a patronym to a matronym if they are discontent with their father. Some people also style themselves with both a patronym and matronym. E.g. Guðrún Ragnars- og Hrefnudóttir: Guðrún, daughter of Ragnar and Hrefna.
In Russia, the patronymic (отчество otchestvo) is sort of like the middle name; it comes in between the first name (имя imya) and last name (фамилия familiya). The patronymic for a son ends in "-ович" ("-ovitch") and the patronymic for a daughter ends in "-овна" ("-ovna"). Socially, a Russian is generally known by his first name and patronymic; a man who is called "Boris Denisov" in court would be called "Boris Grigorovitch" (or whatever) in ordinary life. This can also be a sign that an English writer didn't do the research if they have a Russian character with a patronymic for his last name (or if he has two patronymics).
For instance, the Grand Duchess Anastasia's full name was "Anastasia Nikolaievna Romanova." "Nikolaievna" means "Daughter of Nicholas." Her brother, the tsarevitch (heir) Alexei, was "Alexei Nikolaievitch Romanov" ("Son of Nicholas").
As a small sidenote, while for most daily uses the structure of names followed this model, official documents, as a rule, required the family name to be written first, followed by name and patronymic (maybe a comma after the family name). On envelopes, name and patronymic would often be written as initials (e.g. Romanova, A.N.).
This is one reason why Russian literature can be so confusing for non-natives. The same character can be referred to as Ivan Yanuarevich Petrov, Ivan Yanuarevich, I.Y. Petrov (or Petrov, I.Y.), Ivan Petrov, Petrov, or Ivan. And that's not accounting for diminutives (pet names or nicknames), which could render friend Ivan as Vanya, Van'ka, Vanechka, Vaniusha, Vaniushka, or Ivanushka.
Using one of the Chinese characters from father's name in the names of the children is still quite popular in Korea, even in the North, where Hanjja is not used anymore. Koreans living in the other countries (like Koryo-saram in Russia and other ex-Soviet states) often modify this system by giving their children names that start from the same letter.
Families in Wales used patronymic naming for centuries until very recently. Boys were [name] mab/fab [father's name] and girls merch/ferch [father's name]. This later became ap, which still survives in surnames today.
This explains why so many Welsh family names begin with "P": when Anglicised, the ap prefix attached to the rest of the name and lost the initial "a", so that modern surnames are an echo of the original Welsh. Thus ap Rhys becomes Price or Preece; and so on, generating Pritchard or even Pratchett, Povey, Powell, Prenderghast, Probert, et c.