There are two popular comic strip characters known as Dennis the Menace: the American one created by Hank Ketcham, and the UK one featured in the anthology comic The Beano. Both are young grade-school boys who own dogs and get into mischief, but they're otherwise quite different. To make the coincidence even more astounding, the characters first appeared (in different publications, on opposite sides of the Atlantic) within three days of each other in March 1951.
To avoid confusion the American verison is "Dennis" in the UK and the British comic is called "Dennis and Gnasher" outside the UK.
DC and Marvel each have a character named Atom Smasher (typically differentiated by the Marvel one being Atom-Smasher). In DC, he's the size-changing grandson of the energy-projecting villain Cyclotron. In Marvel, he's the energy-projecting enemy of the size-changing hero Black Goliath.
The two Captain Marvel's.
Only two? Billy Batson, the Lieutenant Marvels (all three of whom happened to share the name "Billy Batson" with the original) Mary Batson, Freddy Freeman on one side, and Mar-Vell, Genis-Vell, Phyla-Vell, Monica Rambeau, Khn'nr, and more on the other... Granted, most of them have alternate names.
To add to the confusion, Monica Rambeau and Genis-Vell have both used the name Captain Marvel and Photon. They at least consciously made the swaps together so you didn't have both using the name at the same time.
There's the alien android who said SPLIT! Who, in what is surely a complete coincidence, had a young friend named Billy Baxton.
Aaannd we have the name Marvel Boy which has been used by a member of the New Warriors (who had an Alternate Timeline double to make things weirder), a teen Marvel superhero from the 50's, and a current Kree hero who is part of the Young Avengers. Marvel Boys have nothing to do with Captain Marvels, though. Neither does Jean Grey who once went by the name Marvel Girl.
That said, the 1950's Marvel Boy had powerful Quantum Bands which eventually went to the hero Quasar who also very briefly took the name Marvel Boy before settling on Quasar. The Phyla-Vell Captain Marvel adopted the name Quasar for a while.
And more recently, the former Ms. Marvel has taken up the Captain Marvel mantle herself.
Which has in turn caused Marvel to recycle the Ms. Marvel identity for a new character named Kamala Khan. She was inspired to be a hero by the original, but other than that there's absolutely no connection between the two.
Multi-Man of DC Comics (debuted 1960) and Multi Man of the Impossibles cartoon (debuted 1966) have surprisingly different powers.
There Can Be Only OneSpider-Man. However, there has been multiple identities of his somewhat "Distaff Counterpart" Spider-Woman: Jessica Drew (black haired, wears red, can float, super power reels more about spider venom), Julia Carpenter (blonde, wears black, can float, super power is more similar with Spidey — about spider web)), Mattie Franklin (seems to be very-directly inspired on Spidey himself, uses spider-legs), and Charlotte Witter (Villainess, white haired, wears green-yellow (a bit like Rogue)). And the Marvel Mangaverse turns Mary Jane into this.
DC Comics has a Batman villain named Scarecrow and Marvel Comics has a villain named Scarecrow (who bounces around Iron Man, Spider-Man, and Ghost Rider's rogues galleries). They even teamed up in Marvel Vs. DC. There is in fact another Marvel villain known as Scarecrow, but now referred to as Straw Man.
For whatever reason, Green Lantern Hal Jordan happens to share a name with his own cousin, Harold "Hal" Jordan, alias Airwave. Yeah, what?
Changeling is either: a minor X-Men adversary from the 1960's who underwent an off-panel Heel-Face Turn and died while covering for Professor X; or another name for Teen Titans member Gar Logan. Both have shapeshifting abilities, but they function differently from each other (the former can change into other people, while the latter can transform into animals).
Morph from the 90's X-Men animated series was supposed to be a modernized version of Changeling, since he technically was an X-Men member in the comics, even if it was only established through a retcon. He even had the same civilian identity of "Kevin Sidney", but the codename "Changeling" couldn't be used at the time since it now belonged to the DC Comics character. Ironically, when the Teen Titans got their own animated series, Gar Logan went back to using his old Beast Boy handle.
In the '1976, Teen Titans introduced a black female member named Bumblebee who could turn herself small, fly and sting bad guys. Years later in 1984, Marvel began publishing Transformers comics, and had been instrumental in developing the characters, hence why I can put them under comic books, and as we all know, there was an Autobot named Bumblebee who would turn into a Volkswagen.
Nightwing used to be Robin, but Nite-wing is a mentally ill man who got his name from a sign advertizing chicken wings all "nite". The latter was a supporting character in the former's series.
Dr. Hugo Strange is both a Golden Age hero and a Batman villain, but neither is to be confused with Marvel's Doctor Strange, who himself should not be confused with one-off Silver AgeIron Man villain Dr Strange. When the GA hero Strange was used in Tom Strong, his name was changed to Tom Strange, probably in part to avoid confusion and otherwise because he was in that story the alternate universe counterpart to Tom Strong.
In the Avengers annual where future X-Men mainstay Rogue first appeared, a little girl, apropos of nothing, introduces herself as "Maddy Pryor," adding "I been sick, but I'm better now." A little while later, X-Men leader Cyclops begins dating - and soon marries - a woman named Madelyne Pryor. Readers assumed there had to be a connection between the two. Actually there wasn't. In real life, Madelyne Prior is the name of a singer with the British folk rock group Steeleye Span. Chris Claremont - the writer of the stories in question - liked the band and used the name as an homage twice, for two otherwise unrelated characters.
Similarly, before the Jubilee we know debuted, there was an unrelated one-shot character with the same name and power (and introduced herself with a similar line.) Evidently, it was a "wanted to reuse that character, but it wouldn't work with the way the older story ended" case.
Fleetway Comics published stories about a kid who played practical jokes on people called...wait for it...Joker. No comment...
Though Word of God is that the robot Vision was created as an Expy when Roy Thomas was denied permission to use the original. The name and costume are meant to be a Shout-Out to the Golden Age version.
There seems to be no relation between Cain Marko (aka The Juggernaut) and Flint Marko (aka The Sandman), apart from the fact that both have fought Spider-Man and were co-created by Stan Lee. Flint Marko's name has since been retconned.
The 1940s Timely Comics heroine Black Widow is definitely not the same character as the more familiar Marvel Comics Russian spy hero of the same name.
We have Daredevil, a Marvel superhero from the sixties who is blind, but has supersenses, wears a red devil-like costume, and fights with a billy club . We also have Daredevil, a Lev Gleason Badass Normal superhero from the forties who wears a red-and-blue costume (split down the middle) and is very good with a boomerang.
In Marvel Comics, Hamilton Slade is the real identity of the third Phantom Rider, a modern day descendant of Carter Slade. Hamilton Slade is also an 18th century vampire in the Marvel miniseries Apocalypse vs Dracula.
There is a G.I. Joe character named Ghost Rider. When Marvel was publishing G.I. Joe comics, they didn't want the trademark getting confused, so his name was never use (there was a running gag that nobody could ever remember his name). Now that IDW is publishing it...the running gag is maintained, because Marvel still owns the trademark in comics.