From what you're describing, this isn't so much physics as fantasy with physics-inspired names. Which is great, because it frees you up to go in whatever direction you want for naming!

For different worlds you could say they had different "topology" or "cohomology" two math-y terms to describe how a world might look.

I quantum mechanics of 2D spaces people talk about "windings", which refer to how many times a particle has been wound around another particle as a way to distinguish them, you could adapt that describe how many times a universe has wound around another universe

Otherwise I think assigning alpha-numeric characters to universes would be a good way to go, possibly complemented by characters giving common ones nicknames - so like Universe a3f57p gets called "ferns" because instead of woody trees evolving ferns just got bigger and bigger.

Sounds interesting, and good luck!