The best way to solve this is not to, and just giving up on the idea of identification.

If you have an infinite multiverse of infinite universes, and perhaps layers on that, with different physics, etc., you can’t have identity outside of all existence.

In Judaism, one/the name of God is translated as “I am”. I believe this is because God’s existence is all, transcending whatever concepts you have of existence or of IDs. That ID is the only ID.

So, the cosmic solution to IDs is the name of God.

which name of god though - there are hundreds, and were right back at the same place of struggling to come up with a unique identifier.