I'm actually quite comfortable with my name, since I'm named after my grandfather and my last name is "fairly" uncommon, i.e. there's very few people that would actually share the same last name in my community.
I would, however, only like to be referred to by my first name only, as my family name is kind of losing meaning in a "he's part of that family" kind of way. We are not 'notorious' in any way, shape, or form, but other members of my family tend to gather friends and followers very quickly, they are very prideful about their surname, and when they fall from grace, they typically try to take down others of our family with them (thankfully, I've been able to avoid this completely, but the stigma still stands).
However, due to the religious nature of my first name, that might not go so well with others. In any case, I have plenty of nicknames and aliases, so I'd just choose the best/common one and go with that.