Before The Legend of Korra premiered, Avatar: The Last Airbender sequel fics would often give Aang and Katara a daughter named Kya, after Katara's mother, and/or a son named Gyatso, after Aang's mentor/father figure. The Legend of Korrajosses the Gyatso one, but confirms Kya as the name of Aang and Katara's lone daughter. Not to mention their eldest son being named after Aang's old friend King Bumi.
It appears that it's expected that if Ichigo and Rukia marry note :pairing that never happened in canon, they'll either have a son with his mother's color scheme, his father's everything else, and the name Kaien, or a daughter named either Hisana or Masaki.
Masaki also applies in the Ichigo/Orihime pairing, but their son is often named Sora. This pairing happened in canon, but the name was jossed; he's named Kazui.
If Roy and Riza have a baby boy, he'll be named after Maes.
If Edward and Winry have a girl, her name will be Nina or Trisha.
Fanfics for the 2003 anime use the above ideas often but also include Ed naming his daughter after "Winry" or Rose naming her son "Edward". Neither die in the series, however the fact that they're split apart in separate universes leaves the same effect.
Whenever Shikamaru has a kid in fanfics, it's pretty expected that the brat'll be named after Asuma in some way. This was jossed in the manga, as his son instead follows the "Shika-" Family Theme Naming.
Naruto himself is not spared this fate; half the time or more his kids would be called either Minato or Kushina. Again, jossed: Boruto and Himawari.
It's not uncommon to see Neji call his son Hizashi.
Many of Sasuke's kids in fanfics are either named after his parents or his brother. In canon, his only daughter is Sarada.
In Corpse Bride fics, Victor and Victoria inevitably end up calling their first-born daughter Emily. Although that's an improvement compared to the author going with the 'V' theme and naming the children something like Vincent/Valerie.
In Fable fanfic, if the author feels the need to give the Princess from the third game a name, chances are they'll have her named after her dead auntie Rose.
Although the closing credits of Pirates of the Caribbean: At World's End give the name of Elizabeth's son as Will (already this trope, of course), a striking number of fanfic writers ignore this in favour of the name James. (Possibly because Norrington is... deader, probably. Or just because of the One Steve Limit.)
In One Piece works, expect many children of Luffy to be named "Ace".
A few Berserk AU fics where the Eclipse never happens and Griffith dies from illness or injuries after his imprisonment have Guts and Casca living a life together with the child Casca was pregnant with in the canon, naming their son after their deceased leader and friend. Some fics take it a step further with the couple having multiple children, with one of their daughters being named after Guts' deceased adopted mother, Sys.
Numerous Final Fantasy VII fanfics engage in this trope, for multiple different characters.
Cloud's son will often be named Zack, and his daughter will often be named either Aerith or Ilfana, depending on who he's paired with.
Jaune's daughter will often be named after Pyrrha.
Ruby's and Yang's daughter will often be named after Summer.
Blake's son will often be named after Adam.
Thanfiction, mastermind behind the "DAYDverse", is especially prone to this. There are only three kids who aren't named after dead people, and two were adopted from another country. Of course, there are a lot of names to choose from...
In the H.I.V.E. Series, Lucy Dexter can conveniently be the namesake of either a boy or a girl, and was conveniently close to both Otto and Laura. In every fic where the two have a child, it will be named after her or Raven.
In "Marie D. Suesse and the Mystery New Pirate Age!", a variant happens. The eponymous character, nicknamed "Mar," vanishes from the world as a result of a wish to restore it, and to fulfill his promise to remember her name, Law names a kitten after her.
In the Total Drama story, Legacy, Heathers baby is to be named after her mothers late campmate.
In Children of Time, Sally (Sparrow) Watson names her firstborn Katherine, after her blasted-to-the-past best friend Cathy Nightingale. "Watson and Sparrow" implies that Cathy was the only real family Sally had.
People Gonna Talk: Zig-zagged in this The Legend of Korra fic. Mako has four children by three different women (It Makes Sense in Context). His twin daughters are both named for living people (his grandmother Yin and Korra's mother Senna), while his sons and Bolin and Opal Bei Fong's daughter all follow this trope: San (named for Mako's late father), Aang (for the previous Avatar), and Poppy (named for her great-great-grandmother Poppy Bei Fong).
In Dante's Night at Freddy's, Dante and Lucia's daughter is referred to as Evie after Dante's mother Eva, and according to its predecessor Revelations, her middle name is Matis, after Lucia's adopted mother Matier. Additionally, their son is named Arthur, which is pronounced similarly to "Sparda", Dante's father.
Both played straight and averted. Grumman asks Roy whether he and Riza plan to name their unborn child after Maes Hughes; Roy replies that there are too many people who deserve the honor of having a child named for them, and so they've decided to give the baby a name all his or her own. Played straight by Ling and Lan Fan, however, who name their first child Fu, after her grandfather.
The final volume of the series reveals that it's also played straight by Alphonse and May Chang, whose daughter is named Nina. Ed and Winry, meanwhile, don't name any of their children after anyone who has died, but one of their sons is named Curtis, in honor of the (still living) Sig and Izumi.
Discussed in a (possibly non-canon) Advice and Trust omake. After Shinji admitted how easily he could turn out like his father if Asuka was killed/comatose, she made him promise that -in the event that she couldn't be with him- he should marry Rei instead and name a daughter after her. He made her give the same promise (although he pointed out that adoption would probably be required under those circumstances).
Alternate Universe Janine's daughter, Elizabeth Joan Watson in The Sanctuary Telepath. Given that she grew up in Victorian Britain it makes some sense, even more so as she can be downright sentimental. Elizabeth was her adoptive mother's name, Joan comes from John (her brother, already dead in that reality) and Watson is the girl's late father's last name (James Watson) which Janine uses for her despite that they've never been married and she uses her brother's last name, Druitt.
It's mentioned in one of the spinoffs to the Frozen fanfic Becoming Free that Freya's childhood friend was going to name her child after her if they were female. Freya isn't dead, however her friend thought she was killed when she was run out of town for being a lesbian. When Freya notes that it's considered bad luck to name your kid after a living person, she questions if maybe they should alter the spelling instead.
In one chapter of the The Loud House fanfic My Sister Leni, Leni finds out that her parents had a stillborn baby that they named "Leni" prior to her.
When Cullen becomes a father in the Skyhold Academy Yearbook series, he names his daughter Eleanor, after his late mother. Later, Cassandra adopts a baby boy and names him Anthony, after her late brother.
There is a Watchmen story where Dan and Laurie's teenage son has the middle name Walter, which was Rorschach's real name. (It should be noted that Rorschach is actually still alive in this story due to time travel shenanigans, but there's no way Dan knew that.)
Pilar's middle name in Starlight Is For Always comes from Jerrica's deceased mother Jacqui. Her given name comes from a relative of her dad's, but it's not mentioned if they're dead or not.
Shadow's daughter Maria in Single Parents Night looks strikingly like Shadow's sister figure Maria Robotnik, who was killed over 50 years ago. The difference is that Maria Robotnik was a human child, but Maria is a hedgehog toddler. It's explained that Maria is a clone of sorts that Shadow found on ARK.
Ash and Misty's son is named after Ash's deceased biological father Will.
Jessie and James' son Skylar married Samuel and Delia's granddaughter Brooke (who is implied to be the child of their daughter Laurel and Tracey). They named their child "Samuel" after his great-grandfather.
In the Sonic the Hedgehog series Descent into Darkness, Maria was named after her paternal grandmother Mary.
In Mind Brigade, Eve names her daughter after Jamie. The two weren't particularly close, with Jamie being a reclusive grouch and the two speaking only a handful of times, but he did inadvertently help Eve decide not to abort and he saved Jill's life after he died by offering in his will to be her heart donor.
In Amazing Fantasy, Peter's daughter, May "Mayday" Parker, after his late Aunt May, who succumbed to old age.
The Great Meta Fic is based on a tournament called Ship Survivor on the RWBY subreddit, with Redditors as characters. Since many Reddtors returned for Ship Survivor II even though their characters were killed off in the first installment of the fic, similarly-named relatives of the original characters represent them in the sequel.