Also, the Joker's true identity is and always should be a mystery. Every time he has a back story in the comics it is different, and The Joker himself has said that he prefers his own history to be multiple choice. Hence in TDK, he tells a different story of his scars every time.

This is one of my fears about Joaquin Phoenix's upcoming Joker movie. When you give him a tragic back story he becomes sympathetic, something the Joker was never meant to be.