It's not unusual, in a face-to-face transaction at a bricks-and-mortar
establishment, that you know neither the legal name of the entity
running the establishment

I'd hope that people can get certs for their actual business name, but sometimes it does differ yes.

However remember that signing in BIP70 is about more than just security, though that's the driving factor. It's also needed for things like dispute mediation, receipts, etc.