Most villains who take on an alias do so to hide their real names or to show they have become the villain or whatnot.
What about the Joker? I know he has a real name because he wasn't always the Joker, but is it ever revealed in any comics?
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The Joker has had more backstories than most people have had t-shirts.
He has a multiple-choice past. (TV Tropes link. You are warned.)
The above pictures show 3 of the histories the character has had, and they aren't even the tip of the iceberg.
He certainly had a real name, but he's so far gone that I doubt he remembers it himself. Most tragically, in one issue of Justice League, the Martian Manhunter takes Batman's psyche to the one place that no one will ever think to look for him (they're being hunted by someone) - the deepest, darkest place in Joker's mind. In it is just one man, who is terrified and alone, not sure where he is or who he is. It's implied this is all that remains of Joker's sanity.
As mentioned in the above answers, there's not a definitive answer. In the "A Death in the Family" storyline, there's a point where Batman scares The Joker into running by implying that he knows The Joker's real name, which he'll reveal, breaking the mystery.
At the end of that storyline, it's revealed that Batman was bluffing and he still has no idea.
The closest we've come to a canonical answer is in Batman: Legends of the Dark Knight issue #50 where a man, Melvin Reipan, is introduced as an idiot savant who actually invents Joker Venom. He addresses The Joker as "Cousin Ja—" before being cut off. Note that "Reipan" is "Napier" backwards and the form of address suggests that The Joker might have a first name of Jack.
But, of course, Melvin dies partway through the issue, so the truth of the matter will likely never be known.
DC claimed that The Joker's real identity will be revealed in issue #50 of DC's Justice League comic on May 25, leading from the revelation in issue #42 where Batman sat on the Mobius Chair where Batman himself learned the identity, but did not reveal it.
The answer there was... not actually a direct answer. Instead, it told him that there were three Jokers, but did not give him names.
We don't know, and neither does Batman. The name plate on the Joker's cell in Arkham Asylum, in the graphic novel The Killing Joke reads "Name Unknown":
(Note that Two-Face's cell reads "Dent H.", highlighting the fact that the Joker's name is a mystery)
In the 1989 Batman Film, The Joker's real name is shown to be Jack Napier. We know this because if you watch the first Batman movie, Batman has a file on Jack Napier because he sees the Joker on his way to where his parents died and recognises his face from when he accidentally let go of Joker in the chemical factory.
The original screenplay explicitly refers to him by this name;
JACK NAPIER : Decent people shouldn't live here. They'd be happier someplace else.
JACK NAPIER is right-hand man and chief enforcer to BOSS CARL GRISSOM.
As well as showing us a copy of his pre-Joker "mug shot";
The Joker's name has been officially* confirmed as "Jack Oswald White" in the comic Flashpoint Beyond #5
* Note that future comics will almost certainly retcon, ignore or outright contradict this factoid.
I read a lot of information, a lot of ideas but.. maybe the answer is there, in front of us.
What do we know so far? The Joker was a man who was forced to be the red hood to make a crime, there is information that he maybe was a criminal in the past. "There were three", well, what if the joker in the beginning was a criminal, running from his past, then he decided to change his life getting married and having a normal life, but everything went wrong and after the accident he became the Joker.
Their identities? Jack Napier (the criminal), Melvin Repian (the comedian), Red Hood (the man who lost everything).
It's just a theory but it make sense.