In the movie.
The Joker is not a person, but a position.
Batman goes to Arkham and finds that the Joker he met in the last movie is escaped. A new Joker (and my dream is Joseph Gordon-Levitt) shows up. Batman, in fact, everyone can plainly see that that is not the same man who was the Joker last time. But there is never any explanation in the movie world for the switch. Or potential switches in the future.