As an aside, I don't see any reason why we couldn't have a system where the combination of someone's name and birth year had to be unique. This would make identifying unique people a snap. Your full name and your birth year would be enough to find your file at the doctor's office, bank, or literally anywhere else.
Even assuming people only choose to pick from the 500 top names, this allows 125 million unique combinations every year following the English trinomial naming convention. It rises to 62.5 billion combinations if one follows the tetranomial Hispanic naming convention. The issue of running out of names or duplicate names would almost never come up. And parents could just reserve a name for their child if they were so bothered.