Does joker know Batman identity

In some incarnations, yes. But in the main Batman story line, the Joker does not know that Batman is really billionaire Bruce Wayne. As said, Joker has deciphered Batman's true identity in a few story arcs, however those tales do not pertain to the the big picture.

Au Contraire, previous poster. While it's been hinted since the 80's "Death in the Family" story that the Joker knew Bruce was Batsy, it was flat-out confirmed in "Batman RIP" in 2008.

That is in fact correct. While Batman "Bruce" was fighting the Black Glove to save Jezebel Jet she kept calling him Bruce while the joker looked on. Batman even removed his mask while freeing her. See Batman #680.