Anytime you have a hero who wears a mask to do what he does, you're going to run into questions of identity. People in this film tend to wear their true faces in their disguises, from Batman's scowl to the Joker's make-up to Two-Face's horrific scars. It leads us to wonder where their personalities end and their accoutrements begin.
Beyond that, The Dark Knight also places a lot of emphasis on how these characters' identities dictate their actions. The Joker's a monster, so he does monstrous things. Batman's a hero because he works to keep people safe, and so on. The interesting thing is that these characters don't always know their identities the way they think they do, and often have to subvert them in order to meet their goals. So Harvey goes from squeaky clean DA to sociopathic menace, even though threads of his psychosis were there from the beginning. Or Batman takes on the mantle of a killer even though it subverts the very justice he seeks to uphold. It can get pretty tangled in those parts of the brain that tell us who we are. The Dark Knight wants to explore as many of those knots as it can.
Questions About Identity
How much do the characters' various disguises (masks, make-up etc.) reveal about their true identities?
Does the public's perception of these figures, whether true or false, help determine their identities? Why or why not?
Does Bruce Wayne's awareness of and acceptance of his dark side help him keep from falling the way Harvey does? If so, how do we see this in the movie?
What does it mean that we know so little about the Joker's identity before the movie starts? How does that focus our attention on who the Joker is rather than who he might have been?
Chew on This
The characters' identity determines their actions here, not the other way around.
The characters are shaped by the things that happen to them, and can't control how their personal history shapes their identity.