Spoiler
Unless the Princess is hiding her own intentions well, I do not think she is the goddess. She seems far too naive and when the PC criticizes the Scarlett Law, she only says it must be kept in place or something bad will happen to Scarlett and doesn't try to defend it. I would assume the Goddess would be more touchy about the curse that she put in place
Azula is a goddess, but she already knows you're a Valla. She says the Valla magic is what can save Rita and is a Valla herself. The only hint I would agree with fitting Azula is getting rid of your if you no longer fulfilled her purpose. She doesn't seem to care much about the PC outside of him being a Valla and being able to give her power.
We are told about the false goddess by someone who's name means "worthless." Not sure if we can just take her word for it.