A few weeks ago, Prof. Williams opened our micro class with one of his random economic thoughts: do you own your reputation? Before you say "of course," ask yourself if you own other people's opinions about you as that's all a reputation is.
The concept is a little strange to wrap your head around because your actions strongly influence others' thoughts. When Tom Cruise acted like an arrogant prick with the Today Show's Matt Lauer a few months ago, the vast majority of the population started thinking of him as an arrogant prick. But that does not mean you own your reputation; if you did, no reputation would go bad. You can only influence it; the effects are ultimately determined by the minds of others.
Similarly, I ask "Do you know your name?" Before you shout back, "Of course, it's MY name!" recall that it's also YOUR reputation; if sementics were a determinant of ownership, I would own my parents. Anyone that's ever been to my house would know that is not the case.
A name is nothing more than a way for others to identify you. The only time you use your own name is to signal to people who you are. Just like repuation, you can influence what you are called, but the result isn't up to you. When P. Diddy renamed himself Diddy for the absurd reason that "the P was getting in the way" of his fans, we all went along with it. We chose to call him Diddy. Why should he own what other people choose to call him?
For contrast, suppose Castro wanted everyone to call him "His Holiness." Or if Mr. Bush declared his new name to be "Gandhi." I can't see society going along with it. You name is your name because that's what everyone chooses to call you. They just happen to call you the same thing.