It should be up to each PNM what she decides to do.
I would like to know, as the PNM goes into rush, what sororities are represented at her school - but if she's not comfortable sharing that info, that's fine.
I do like the idea of assigning names to the sororities - it's less confusing than numbers. I would only suggest that (1) the names be consistent, and (2) they have nothing to do with the sororities themselves (using colors and calling AEPhi "green", Alpha Phi "bordeaux", etc. would probably be a dead giveaway
). After rush, the PNM can come back (if she wants) and tell us who's who, so we sorority members can learn from our mistakes.