A popular example (and, obviously, the Trope Namer) is Shazam, the title used for most works involving DC Comics' Captain Marvel (pictured on the main page). Due to a trademark agreement with Marvel Comics, DC cannot use the character's name for the series title but can for inside the comic itself, so they use his transformation phrase instead; this leads to people mistaking the phrase for his name. This is especially strange, considering he himself has to be careful about using the phrase—"Shazam!" always summons a bolt of magical lightning whether Billy means to transform or not (or that's the case pre-New 52, anyway).
This is exacerbated in the Hero Clix game, where any of his figures have to have Shazam written where the name is instead of Captain Marvel.
This seems to be the case for almost any DC-licensed product he appears in, as promotional material for Mortal Kombat vs. DC Universe referred to him as "Shazam" as well, but the game itself used "Captain Marvel".
A 1970s "dry look" hair product commercial labeled Captain Marvel as "Shazam."
A humorously similar case occurs with CM3, originally Captain Marvel Jr, a DC character who himself briefly changed his superhero name because the original starts with his magic phrase (which is "Captain Marvel"). This was also highlighted in a possible future where he eventually became Captain Marvel, which he, of course, couldn't say.
Recent developments in The DCU have had Captain Marvel take the (late) wizard Shazam's place, with CM3/Captain Marvel Jr. being groomed to take the role of The Hero — with the codename "Shazam".
MAD, produced by Warner Brothers (which owns DC) averts this trope, but in a couple of sketches they refer to Cap as "Shazam" for the sake of a joke; for example, in the "Superfriends" song, they use it because it fit the song better than "Captain Marvel".
Captain Marvel has recently had his name changed to "Shazam" in the New 52, where he was reimagined as a grittier, more relatable character. He starred in the Curse of Shazam! miniseries presented as a back-up feature in the main Justice League book, and has since started to appear in the Justice League books. As he now needs to specifically channel his willpower (his "intent") while saying "Shazam" for the spell to work, he doesn't have to worry about summoning lightning bolts every time he introduces himself.
Shortly after this it was announced that Carol Danvers would start headlining a new Captain Marvel series for Marvel, with a potential live-action film in the works as well. Word of God claims the timing was a complete coincidence though.....
The title of Alan Moore's Watchmen is thematic and poetic, not literal; there is a team of heroes called the Minutemen and a later, failed attempt to form one called the Crimebusters, but there is no team called the Watchmen.
The movie actually does rename the Crimebusters "the Watchmen", thereby both averting and exemplifying this trope.
Though even in the movie, the title is something of a misnomer since the Crimebusters/Watchmen were a proposed team that never actually formed. The five main characters never make up an organized superhero team — for the most part, they're just independent vigilantes who form some close personal relationships. Nite Owl and Rorschach are the only characters who regularly fight crime as a team.
The lead character of Neil Gaiman's The Sandman goes by many names, but "the Sandman" is never one of them. The closest he comes to acknowledging this name occurs when he is moved to laughter — for the first and only time in the series, and even then, with a mask covering his face — by the presumption of a human superhero calling himself "the Sandman". There's a certain irony in this, as the superhero Sandman comes from an older, defunct DC series; although in the continuity of Sandman Morpheus is of course much, much older than Hector Hall, in real chronology Hall had the title first.
The third published collection (or one version of it anyway) contains a script for one of the stories along with commentary by Gaiman. He mentions that he always refers to the character as The Sandman himself, as well as in the script. He never mentions why other characters don't do the same, though.
John Constantine has probably come the closest, since at the end of one crossover, he walks away from an encounter with Morpheus singing "Mister Sandman."
He got the idea from Mad Hettie.
Mad Hettie: 'E's back, John. Constantine: Who's back, Mad Hettie? Mad Hettie: You ort ter know, smart boy. Morpheus. The Oneiromancer. You know... The Sandman. They continue to refer to him as "The Sandman" throughout the conversation.
Neither Eric, nor any of the later vengeful souls from the comics or films of The Crow, are ever referred to as "The Crow". The title refers to the bird that brings them back to life. They go by the names they held in life, if anything (though the crow in the original comic constantly refers to Eric as "Musician" or "Kid").
In the TV series, "Crows" are what the series calls the "good" avenger-type revenants like Eric, whereas the "evil" sadist/hedonist-type revenants are referred to as "Snakes".
Eric actually does refer to himself as "The Crow" in the comic when speaking to police, although it's more of a thinly veiled clue than a superhero alter-ego. (His last words, heard by the police captain, were "The crow said don't look!")
The star of Usagi Yojimbo is actually called Miyamoto Usagi. The title, which translates to "bodyguard rabbit" is what Usagi does. The series isn't helped by the fact that, during the character's appearances in the first Teenage Mutant Ninja Turtles cartoon, he was referred to as Usagi Yojimbo.
Runaways is the name of the book, not the name of the team. The kids do not have a name for themselves, just like they do not have costumes or code names. This is made more confusing because most fans do refer to them as "The Runaways", mostly because it is easier than saying, "those teenagers that star in the comic series that is called Runaways." The problem is exacerbated because Nico (The sort-of team leader) does at one time address the group as "Runaways" (With the statement "Runaways, run away!"); she is using the term as a description of the people on the team (Who are all teenage runaways), rather than as an identifying name.
Nico as least seems to consider Runaways the team name, given she used it again recently, and it was capitalized.
Other characters refer to them as "Those Runaways" or "Those kids in LA" or "The Pride's Kids" keeping with the idea that they don't have an official superhero team name.
Birds of Prey is not the team's official name, and was not even spoken in dialogue until issue #86 of the series, wherein Lady Blackhawk sugested it as a potential name. In later issues the characters specifically said that it was not their team name when Zinda Blake continues to use it, and it has never been used on "official" business (i.e. the induction of new members or cooperations with other superteams). However, the writers themselves often seem to forget this point, as numerous characters (Both on and off the team) refer to them as 'the birds' on a semi-regular basis, and the full "Birds of Prey" title itself makes an occasional appearance.
Similar to the Birds of Prey example, Uncanny Avengers is the title of the book, not the actual team featured. The team itself is referred to as the Avengers Unity Squad, while the title of the book is just a Shout-Out to the iconic Uncanny X-Men series.
The team of heroines in Fearless Defenders aren't actually called that; they're known as the Valkyor. The series' writer, Cullen Bunn, has admitted in interviews that his editor basically slapped "Defenders" onto the book due to the name recognition factor.
Technically, the official name of the city is Basin City. Sin City is simply the nickname everyone including the inhabitants of said city call it, so, yeah, this one's OK.
"Witchblade" is the name of the weapon/bracelet/thing, not the person wielding it. But plenty of people seem to think Sara Pezzini or Masane Amaha are named "Witchblade".
It has become a running joke for the character Araņa, who as of late has been mistakenly referred to as "Spider-Girl" by numerous characters. Even in the face of her impending execution, she angrily tells her captors "The name's Araņa," after they take the gag off her mouth in order to let her give her last words to the camera. By late 2010, she goes by the name of Spider-Girl.
Enemy Ace is the title of the DC Comics feature starring Hans von Hammer. Von Hammer is never actually referred to by that name (except generically - to the Allies he is of course an "enemy ace.") His actual Red Baron moniker is "The Hammer of Hell."
In a weird story arc example, the famous Iron Man story arc "Armor Wars" is actually called "Stark Wars", despite what the trade says. (It was intended as a Star Wars pun.) Even Marvel got this wrong, or at least Retconned it—they commissioned and advertised an "Armor Wars Part II" storyline, and the readers knew exactly what they meant.
Also, the two different "Stark becomes an alcoholic" stories often get conflated as one arc, "Demon In A Bottle". That story is only the early one from 1980, in which he kills the Carnelian ambassador and sobers up rather quickly. The multi-year arc in the mid-80s where Obadiah Stane is the villain and Rhodey becomes Iron Man for the first time has no real name, although some fans call it "Demon In A Bottle II".
In The Mask, anyone who wears the title artifact is called "Big Head" - unlike in the movie and derivated material, where masked Stanley goes by "The Mask".
The Black Panther villain Kiber the Cruel is only called Frederick Kiber or just Kiber in the pages of the Panther issues in which he appears. Although he is evil and murderous, none of his victims lives long enough to spread the word of his cruelty, which the usual method in which evil men get such colorful monikers. The origin of this moniker is an issue cover blurb that says "Sinister are the Servants of Kiber the Cruel!". Kiber's entry in Official Handbook of the Marvel Universe as well as other publications do list his entry as Kiber the Cruel, however.
Captain Atom's splinter Justice League in the '90s? They aren't actually called "Extreme Justice," you know; that's just the name of the book.
Slam: No, see, the thin man was the murder victim. They were looking for the thin man.
Selina: I though the thin man was the hero?
Selina: Then why did they call all the rest of the movies The Thin Man This and That?
Slam: Because Hollywood is full of idiots.
Played with in an issue of A + X, where Deadpool teams up with Hawkeye. At one point, Deadpool is about to call Hawkeye "Legolas" before he shoots that down. Then he calls him "Hunger Games"note most likely trying to reference Katniss, which gets shot down, too, and "Brave! The girl from Brave!" Yep. Shot down.