By that logic, forcing any name on a child is selfish, so they should pick their own name, since they are the ones that would have it. Although, in that case, temporary names would probably be a thing, so I don’t really see the issue (or you could use other cultural naming conventions like that, but that is one that exists.)
Unless your argument is nonconformity is selfish? I personally think some people will find a reason to make fun of another person, but nominative determination does have its appeal if you don’t believe that.
All names were unique at some point, but that’s a moot point. Eventually they will either become more popular or less popular.
Be careful what you wish for, or they will find the one woman trained in medicine who wants to sterilize people using logic derived from eugenics.