I hope you come back and let us know how it goes. It seems to be pretty hard to find a good trauma t to work with and I really hope it works out in a way that will be really helpful for you.
My new t knows my diagnosis because she met with previous t last week so ex t could share info about me including diagnosis history and work in therapy so far. I am not entirely comfortable with that because I still have a lot of amnesia and I know parts of me told ex t things i don't know about it.... which means I don't know about all the things that ex T told new t and I don't like that feeling. I gave permission for that though so i can't complain about it.
But in my session with new t this week (2nd session like you) I was so dissociative and constantly switching from one to the other so even if they hadn't shared info I don't think I could have hidden it anyway.
And for you if you still have DID there probably isn't any way you could hide it in therapy for long no matter how much you yourself don't want to focus on parts. If they are there they will have their own opinions on that and will come to therapy sooner or later and it looks like its happening more on the sooner side!