Oedipus Rex

My question is somewhat relevant to Oedipus Rex. Oedipus lives his life thinking that he knows who is parents are, but they actually are not. He was royalty during the entire play, so that bit of his life was unaffected by the parent swap. Oedipus could never 100% know who he is because he killed his father and his mother killed herself, so he could never know his whole history.

The Big Question . . .

Can you every truly know who you are and how do you go about finding who you are anyway?