I think the concept of keeping a “bad” name was addressed best in the movie Office Space:
Michael Bolton: Yeah, well, at least your name isn’t Michael Bolton.
Samir: You know, there’s nothing wrong with that name.
Michael Bolton: There *was* nothing wrong with it… until I was about twelve years old and that no-talent ass clown became famous and started winning Grammys.
Samir: Hmm… well, why don’t you just go by Mike instead of Michael?
Michael Bolton: No way! Why should I change? He’s the one who sucks.