As in real life, there are all sorts of people with the same names in the world that don't know each other, or have any direct relation. I don't see how it's any different in a fantasy world either.
Regardless, if a persons "unique" Legacy name is worth being copied (deliberately, or not) by other players, it probably wasn't very unique an idea for a Legacy name to begin with.
Take heart though, your characters first name will stay "unique".