People generally aren't considered to have the right to divorce themselves from their past identities. Most jurisdictions make name changes a part of the public record, for instance.

I can think of at least two ways in which a central registry might be slightly useful: (1) to help law enforcement identify people who committed crimes before legally changing their identity, and (2) as a quick way to narrow down who to contact for important health information.

There are presumably other ways to do either of those, but those are also available to the genocidal and rights-denying.