As does their county of birth, parenting, era of birth, physicality, intelligence etc etc... What can not influence who you become? Everything including who your neighbours were. The kind of pets you have had. Everything bring you to THIS moment.
And just to tweak this debate, you have no choice in who you become. It is destined.
Of course, a person's name and their physical appearance dictate how the world sees them. This is why so many people legally change their names and get plastic surgery. Everyone can make choices about the way they live their lives and how are seen. People can choose their clothing, and they can make nicknames for themselves, too
Just because someone looks a certain way or has a name given by their parents it does not mean that they will live a certain lifestyle. It is the lessons that the person chooses to listen to as well as the actions that the person chooses to take that define who they become.