The Phantom, An In-Universe example: The Skull Cave has The Small Treasure Room, an enourmous cavern filled with gold and jewels amassed by 21 generations of Phantoms that are freely given away to people in need and The Big Treasure Room, a relatively snug room filled with bookcases and display cases filled with yes, priceless artifacts, but also relatively useless trivia (say a 16th century Swedish snuff box) from generations of adventures.
In Marvel Comics, the original Human Torch was neither a human nor a torch but an android that burned on contact with air. The reason for his odd name is that at the time, "human torches" (performers who lit themselves on fire) were a well-known circus act. Since they're rarely seen today, modern readers parse the words separately and get confused.
In Universe-X there were Human Torches. They were torches but they weren't human.
There's a Human Robot who, to all appearances, is merely a robot and in no way human. In his revived version this is because the scientist who built him transferred his own life force into it. So the name is in fact accurate, but its meaning is not apparent to an outsider.
Doctor Doom is not actually a doctor, but Fan Wank says he might have given himself an honorary one as ruler of Latveria. It should be noted that Doom himself almost never calls himself "Doctor" Doom, but simply "Doom" (ALLCAPS optional).
Of course, his archenemy, Mr. Fantastic, has several doctorates. He's generally addressed as "Dr. Richards".
While Iron Man's prototype suit was originally iron, the material of other versions has varied depending on continuity. In most of the comics, the suits have had iron in some form in the outer shell, usually enhanced in some way with forcefields. In some continuities, it's explained that Tony was inspired by the Black Sabbath song, though ironically the lyrics describe a Fallen Hero (and the comics hero himself predated the song by seven years).
In the movies, this is Lampshaded (the explanation is used in the novelization, and carried over to the movies proper with a nod in the Avengers movie, where Tony wears a Black Sabbath shirt).
Stark: "Iron Man". That's kind of catchy. It's got a nice ring to it. I mean it's not technically accurate. The suit's a gold titanium alloy, but it's kind of provocative, the imagery anyway.
In the Dutch translation, he is known as "Steelman". His suit probably isn't steel either, though.
The word 'warlock' comes from the Old English 'waerloga', "oathbreaker", and originally referred to any practitioner of magic (who had thus broken faith with the church). Since Warlock defied his father and his home planet's traditions when joining the New Mutants, the moniker "oathbreaker" fits him rather nicely.
Warlock's father, the Magus, is (obviously) also a robot alien. Not an astrologist or magician.
The Marvel Comics character now known as Wiccan (who is one of Scarlet Witch's reincarnated twins) was presented with "Warlock" as a possible codename. He immediately rejoins with the "oathbreaker" argument, concluding with "it is not a nice word."
In Marvel Comics, you'd think with a name like Typhoid Mary, this occasional Daredevil villain would have some kind of 'walking plague' power set. But that's far from the case, she's actually a mentally ill telepath with telekinesis/pyrokinesis. She just wanted a tough sounding name to declare that no man is ever going to abuse her again.
In Watchmen, The Comedian, despite his name, never actually says or does anything funny. He understands what a joke society is, and becomes a parody of it. Could be justified, as "The Parodist" isn't nearly as good of a superhero name. Granted, he originally wore a jester costume and had a smiley, happy-go-lucky attitude, but whatever.
In the Great Ten, well... Immortal Man in Darkness couldn't be a less accurate name if it tried because the technology of the plane he flies drains his life as he pilots it; there have been about seven Immortal Men in Darkness since the team was founded. The name is a publicity thing. Similarly, the Seven Deadly Brothers. "I am seven. I am deadly. But I am a brother to no one." This is because the Seven Deadly Brothers are actually one man, an only child at that, who splits into seven people with different personalities due to a curse.
One Flash story arc is called "The Dastardly Death of the Rogues". There's only one death, and it's not a Rogue.
The Silver Sorceress, a DC Comics character introduced in 1971 as a deliberate Captain Ersatz of Marvel's Scarlet Witch, wore a costume that of course... consisted entirely of gold, brown, and red shades. When she became part of the Justice League over a decade later, she did have silver hair at least, though it was completely covered by her elaborate headgear and a Retcon in any event — in her first appearance, she was depicted with brown hair.
Somewhat justified in-universe: in her last major appearance, before her Heroic Sacrifice, she admitted to being colorblind.
Another Justice Leaguer from the "International" era, the Crimson Fox, wore a costume consisting of brown and black shades, and no crimson whatsoever. She was originally going to be called the Red Fox (which is more fitting since her suit does look sorta red Depending on the Artist), but the possibility of legal action from the creators of an indie comic called Redfoxnecessitated a name change on DC's part.
Maybe one day we'll find out what The Avengers are supposed to be avenging. In-universe, the name was picked pretty much entirely for Rule of Cool.
Lampshaded in the movie, where as Agent Coulson lies dying he says that he's okay with it, as the team would never work without something to... well, he ends there, but "avenge" is implied. Later on, Iron Man states that if they can't save the world, they will avenge it. Prior to that, "the Avengers Initiative" was just SHIELD's codename for the program.
The X-Men's resident card-obsessed Badass is named Gambit, even though "gambit" is commonly used as a chess term. However, "gambit" is conversationally used outside of chess contexts, e. g. in debating, to refer to a calculated maneuver in general. When the priest Ruy López de Segura introduced the word into the language of chess in 1561, he used an already existing term from Italian, dare il gambetto. This came from the language of wrestling and meant "to use your leg to trip up your opponent".
The Sinister Six in The Superior Foes of Spider-Man suffers this, as there are five of them. Boomerang defends this to the other members by claiming that it will make people think there's a secret sixth member, who could be anyone. It could be Dormammu (A demon lord vastly more powerful than all of them combined)!
The title Superior Spider-Man ultimately proved to be non-indicative. During the final arc, Octavius was forced to concede that he was, if anything, inferior to the true Spider-Man, Peter Parker.
In 1944, Harry "A" Chesler publications introduced a character called Dr. Vampire. He was actually a Vampire Hunter, not a Vampire.
Firestorm's powers and origin have nothing to do with fire, weather, or firestorms, unless you count nuclear "fire". His main ability is molecular-level transmutation.
DC's Vigilante (Adrian Chase) occasionally fought a pair of assassins named Cannon (who wielded blades) and Saber (who used guns).
Spawn: recurring cop character Twitch is a skilled marksman with nerves of steel and a steady hand. In one issue it's commented, "The reason they call him Twitch is because he doesn't."
Crops up a couple of times in The Multiversity in regards to certain Earth-8 residents and their Earth-7 counterparts.
Wandajin is the name for a group or cloud and rain spirits from Aborginal Mythology, yet the superhero from Earth-8 with that name is white, whilst his counterpart on Earth-7 who is aboriginal is given the more generic moniker: Thunderer.
Another superhero is named American Crusader and whilst he does have elements resembling a Holy Crusader, he doesn’t have any design elements that say America. Contrast this with his Earth-7 counterpart Crusader, who lacks the American part of the former's name, but is near-identical to UltimateCaptain America with the Wearing a Flag on Your Head slightly toned down.
And as seen in her apparition in Marvel Divas, she isn't against attending at high noon either.
The Fox Hunt has the villain who refers to himself as "Brontosaurus", despite being a tall, orange, humanoid person/thing that possessed a bank robber to lay low and has nothing to do with dinosaurs whatsoever. A couple of the characters calls him out on this.
Nightcrawler of the X-Men has nothing to do with worms. His body is covered in dark blue, nearly black fur, which is probably where the "night" part comes from. However, he's trained acrobat and does a lot of jumping around and not much crawling. He does crouch, however.
The Ten-Seconders: "Hero" is the leader of the Gods, but he's more of a supervillain than a superhero, being a tyrannical maniac who spearheaded the destruction of human civilization and keeps at least one of his fellow Gods in captivity.
The Uglydolls comic "So, You Want to be A Ninja", has Ninja Batty Shogun training Wedgehead in the art of ninjitsu, part of which involves giving different and wildly incorrect names to things that already exist. Ninja Fries and Ninja Ketchup are actually onion rings and sweet chili sauce, while Ninja Tacos are microwave burritos. Do not question your sensei!
When the character Gwenpool was introduced, Marvel fans were disappointed to find out that she wasn't Gwen Stacy as Deadpool but rather a person named Gwen Poole.
On a meta level, this often applies to comic titles themselves. In the 20th century, publishers frequently had good reasons to maintain the continuity of a particular title even as its contents changed. This happened a lot at DC in the Golden Age; Superman appeared in Action Comics; Batman started in Detective Comics. Marvel took its turn in the Silver Age, debuting a lot of classic heroes under non-indicative names: Tales to Astonish = Ant-Man, Tales of Suspense = Iron Man, etc.