The mom has the right to the mom name.
I am more circumstance-dependent than you on this issue (if the case plan was termination and there was no visitation, as with one of Katherine’s adoptions (and thanks for the name tip), I wouldn’t treat a foster-adopt baby any differently than a privately adopted baby in terms of how/when I talked about the adoption).
I dont know about other people, but i havent done any "foster-adopt" adoptions. My kids were foster kids, until i adopted them. And until those adoption placement papers were filed with the court (and really, until the adoptions were final) my kids were FOSTER kids and i needed to keep that in mind. With my first adopted son, i knew from placement that if i got to adopt, i would change his name. But i couldnt start calling him by a new name until much further down the line. The agency/workers called him by his birthname until finalization (in fact, they called him that even after, grr.) Its a very fine line to walk, when you are fostering a child you think you'll be able to adopt but before you are the adoptive parent. With my first, it wasnt until he was about six months old that it was decided that i was the only adoptive resource, the relative was not pursuing adoption, and the worker asked for his new name for the paperwork she'd eventually file. I felt comfortable at that time calling him by his adoptive name. (Before that i just kinda avoided the issue by calling him "the baby" a lot)...we didnt finalize until he was nearly 11 months old and at ANY time the agency could have decided on a whim to move him to a new home and there was little i could do about it.
I realize other states may operate differently.