Kate in KateModern revealed in the fourth episode that her name wasn't really Kate. Her real first name, Genevieve, wasn't revealed until episode 88, "Birthday Surprise", while her surname, Strathcarron, wasn't revealed until episode 163, "Prime Suspect". Several other major characters' surnames have not been revealed, including Charlie, Lauren, Sophie and Terrence, but it is not implied that there is any mystery behind those names.
There's also the Watcher and the Shadow, whose lack of names befit their status as anonymous Order agents.
An anonymous member of Danya's terrorist organization is never referred to by name by his colleagues. On the board, he's commonly called 'The Mystery Man'.
In Tales of MU, the ruler of the old empire is always referred to as The Unnameable One. One of Mackenzie's professors also has never been named in canon, but that's more of a subtle Running Gag.
MUniverse tradition has it that the sound denoted by "kh" is reserved for the names of the gods, and that it is blasphemy for anyone who is not a god to have it in their name. As an immortal vampire, the Unnameable One is old enough to predate this tradition, and is named Khulrakh.It is blasphemy to call him by his name, and an insult to a sitting emperor to call him anything but his name. Thus, he is Unnameable.
The title character of Pittsburgh Dad hasn't been given a name, though his wife (Deb) and next-door neighbor (Tom) have.
In Day of the Choosing, none of the characters have names. Even the Big Bad's name, "All the Rest," was created on the fly by the protagonist.
None of the characters of Fanpro have official names. Naming them seems to be optional in fan works, and they are generally just distinguished by their numbers.
It took 33 episodes of Welcome to Night Vale for Cecil's full name to be revealed (it's Cecil Gershwin Palmer. Probably). Carlos the Scientist, Intern Dana, Old Woman Josie, Telly the Barber, and Kevin are all still going without surnames. Some characters, such as The Man In The Tan Jacket, The Traveler, and The Faceless Old Woman Who Lives In Your House, don't have names at all, and all the angels are simply referred to as "Erika."
Manatee Girl: The Movie has Hunky Marine Biologist Boyfriend...who is known only as Hunky Marine Biologist Boyfriend.
Played with in Killerbunnies, as technically, any Killerbunny born, raised, or used in a lab for laboratory use don't normally have names, aside from their identification codes, which wouldn't be a name, unless it is counted as such, as would be the case with Test Subject 001892300012 ("Lucy"), Experiment XI0014101 ("Marigold"), Child #999 ("Lilith"), and Subject 200167 ("Mango"). However, this, according to Word of God, is subverted in the case of Michealenne, as that is the name on one of her ID tags.
In the SuperMarioLogan series, a recurring character with many different jobs and a thick Brooklyn accent is reffered to as "The Brooklyn Guy". In "Bowser Junior Loses Thomas", he works as a Toys R Us employee. When Chef Pee Pee asks him where his name tag is, he states that he doesn't have a name tag because he doesn't have a name.
Finding Hope, as an homage to classic Spaghetti Westerns, gives us "Nobody" and "Jack Angel", both of which are aliases. In Nobody's case, he gave himself that name as a way to represent his status in society.
Petscop: This applies to both the uploader of the videos and the game's protagonist. There is no clear name given to either of them. At the beginning of the first video, the uploader names his save file "Paul", but it is unclear whether it is his own name or the name he wants to give to the protagonist. For the protagonist, in video 5, the strange artifact known as "TOOL" answers the question "Who am I?" with "Newmaker". This answer is vague, as TOOL is not clear who is named "Newmaker". Despite this, fans have just taken to referring to both the uploader of the videos and game protagonist as "Paul". In order to differentiate between the uploader of the videos and the game protagonist, a popular solution is to refer to the video uploader as "Paul" and the game protagonist as "Naul", a combination of "Newmaker" and "Paul".