Recently the BBC declared Some Like It Hot the greatest film comedy of all time.  Here's the essay.  An excerpt about how the film plays with identity:

Look again at the beach scene with Joe and Sugar. It was written by two men who were once called Samuel Wilder and Itec Domnici, and acted by a man and a woman who were once called Bernie Schwartz and Norma Jeane Mortenson. Schwartz, who renamed himself Tony Curtis, is playing Joe, who is pretending to be Junior, using the mid-Atlantic vowels of Cary Grant, who was once called Archibald Leach. Mortenson, who renamed herself Marilyn Monroe, is playing Sugar Kowalczyk, who renamed herself Sugar Kane, and who is using lines which Joe used when he was pretending to be Josephine. Not even Twelfth Night or The Importance of Being Earnest had such elaborate fun with its characters’ identities. Names, genders, social standings ... they can all change in Some Like It Hot. It’s the American way.