Hi wisewoman,
i agree that labels are so not important. The only thing that really matters is that if you have separate parts your T needs to know and acknowledge it. If your T doesn't realize that there are separate parts he or she may say things that little parts shouldn't hear or imagine that the part present has the same views about everything as you do - or all the other parts do.

Therapy for DID is more like group therapy and if your T treats all your parts with the same attention then it doesn't matter what they call it for the insurance. It's much better if there's a way to technically not be given a label that will limit you in the future- because of the misunderstanding of others and even limit employment,etc.
i could never go to a T that didn't understand that what 'i' say is not what all of me believes and there are opposing parts to every part in my system. They need therapy also. Also my little ones- age 8 and under- can't hear some thing that the adults can. They would not understand at all. If you switched to a child part and were not able to drive or felt lost, then your T should know how to help you be adult again and get your bearings .
The most difficult thing is that the therapist might imagine that you agreed with everything that 'you' said.
Parts talk that disagree and would confuse the therapist that didn't acknowledge that you have DID.
The therapist has to address each part to find out all the ways that you feel about something or it's a confusing mess that doesn't get you anywhere.

i hope that it works out and your T understands you.

Take care (((((wisewoman))))) safe hugs if ok,
kerria