I am totally fine with Chromie knowing Rin's names, as well as any future characters should I app them here.

Potential spoilers for Unlimited Blade Works here:

Also I was going to leave it at that, but since time IS Chromie's bag, Rin does have a pendant she usually keeps in her pocket that is both explicitly tied to her existence, but also comes from a different timeline and has in fact existed outside of time for a long-ass while before it found its way into her pocket. (hard to quantify how long, with said outside time's existence) If you want to do anything with that, though, feel free to!