Generate a user name for the user. One can do that such that the probability of the generated name matching that of the user essentially zero. For example, a SHA-256 hash, hex printed, is highly unlikely to match a real name, and even if it does, it likely has a less than a billion chance of being the name of the person you give it to.

If you limit yourself to three-part 'normal' names, there may be some matches, but if everybody knows user names are doled out randomly, I don't think that matters.

For the Facebooks of the world, I doubt using pseudonyms matters, though, as they will soon discover who's behind each pseudonym, even if a third party assigned them, if only because your alias will be in the address book of your friends.