I think what could work is requiring users to prove their authenticity and uniqueness using a national ID of some sort. It would be bad for privacy, no doubt, but it surely would work. But the users' actual names should not be displayed.
Sites and apps don’t need your actual national ID, just to know that you have one. I think it could be possible to have 3rd party verification services that don’t know where the verification request is coming from, thus preserving privacy on both sides.