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?
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 closes 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.
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";
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)
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.
Joker's name isn't Jack Napier. That was actually a name given to the character played by Jack Nicholson by the screenwriters.
When the character was created originally he had no name besides 'The Joker' to give the character a bigger sense of creepy, craziness, and a sense that he's plainly just-not-right in the head. In fact, The Joker was never given a normal name until the Batman movie starring Michael Keaton and Jack Nicholson, just so they could provide a longer back-story in the movie.
First he was an engineer,who tried becoming a comedian, but failed.then he joined two criminals to make money until his pregnant wife died, so the two criminals make him put on the red hood mask. He then falls into an experimental vat that permanently bleaches his skin white and his lips red, and dyes his hair green. The fact that this happened was enough to turn him into an insane criminal in Gotham, leaving him to be an enemy of Batman. Still, they don't reveal his name. It was both a movie and a comic. In fact, I just saw it a couple weeks ago. His name was Jack Napier, but a different Dc Universe.
After extensive research and multiple surprise phone calls to numerous people, I have devised the name originally intended for The Joker to have. The name Terrance Kemp was originally supposed to belong to the man now known as The Joker. In the comics it was originally intended that The Joker, being killed off after his first appearance, Batman was supposed to be called on to investigate his chemical studies on account of the unusual amount of chemicals that he had access to. After the writers changed their minds and decided to keep him in the series they simply never got around to adding his back-story into the comics.
I did not search the internet only interviewed many people over phone as well as face-to-face. In almost all cases I have been asked not to reveal the identity of said people in order not to have questioning fans and publicity problems. I am sorry if you do not believe me on account of a lack of links even though it is completely true.