I recently saw a provider who posted under one name and then answered my email by another. She explained that she was changing her identity because of a falling out with a client/boyfriend who threatened to out her and to please use only her new name in any review I might post.
Ok, no problem but then I see her advertise on another site with the name that she asked me not to use so I don't want to cause her any grief but if she is playing some kind of game that is something that potential clients have a right to know about no? Any thoughts?

The situation could be very complicated or even dangerous to the provider.  One senario for you to consider: she may be changing her identity and still maintains ads under her former name to throw off the person she is trying to avoid...

If she was a sweet, welcoming, seductive and satisfying provider- I wouldn't suggest burning your bridge with her.  Puss is everywhere. Good Puss, that fits you just right and makes you feel amazing afterward is a different story.