[barakm]

You’re right to go to Planck length to get a number of bits to represent an atom, but here’s another angle:

To best guess, there are about 10^24 stars in the sky. That’s about 2^80.

That means you could simply, on Earth-prime, give an id to all the stars in 2^944 universes. Way way less than the multi-multiverse in question, let alone anything atomic.