User blog comment:MakeShift/The Crisis and its impact on the Arrowverse Wiki/@comment-38932496-20200124013401/@comment-4996626-20200127074023

But I would argue that Alex Danvers did, in this new multiverse in this new timeline originate from Earth-Prime. She only regained the memmories of the Alex from Earth-38, hence the double "Home Earth" for such characters.

If we take another example like Weather Witch. She does not have any memmories of Earth-1. So for her she has always existed on Earth-Prime. But I don't think that she is intended to be a doppleganger of Weather Witch (Earth-1). I think she is intended to be the same character, with (almost) the same backstory, just moved to this new multiverse.

So my suggestion: Characters born on Earth-Prime in this new timeline should have their home earth as "Earth-Prime", but also regain the Home earth of their life in their previous multiverse.