Yes, it was explicitly said that Gluttony only ate her "memories", not her "name". In contrast, Rem's "name" and "memories" were eaten, leading to her comatose state. Gluttony probably spared Crusch's "name" because they need her awake for some nefarious objective.

I do think they can get those things back if they manage to murder Gluttony. Otherwise, there is no reason for Rem's body to remain alive.