Oedipus Rex was born with a horrific curse that said he would kill his father and marry his mother. But did that prophecy truly define his identity? Was his fate like an unescapable genetic disease? Though there are some things that you're born with and stuck with forever, I don't believe this curse ultimately defined Oedipus. He had a great identity going for himself until mention of the curse came into his life. He was a good, strong ruler of his land, and I think his flaws -emotional immaturity and excessive pride- were what ultimately ruined him.
Thank God that I was not born with such a curse, but we all have reputations and family characteristics that follow us throughout our lives and possibly give others a false sense of our identity. A simple but common example is the kid brother of the superstar student athlete that all the teachers adored. He is probably going to get fed up of constantly being placed his older sibling's shadow. But I think that if your character is strong enough, then it is 100% possible to overcome preconceptions and show your own unique qualities.