So, this is something I asked potential T's when I briefly terminated with my current T in September that seems like it would be relevant in your case:

Would you feel comfortable discussing what happened with my former T and helping me process the termination?

And if you'd rather not disclose your T's name to them, ask if they'd be OK with that. If you do plan on mentioning your former T's name, you may want to find out if a potential T knows that T personally and/or professionally and if they'd feel comfortable discussing stuff that happened with them in your therapy. (I learned that current T used to work with ex-MC and ex-T and, though I originally wasn't going to mention ex-MC's name, realized that if I talked about a particular thing--his wife passing away--current T might know who I meant. So I did end up telling him his name and asked if he'd feel OK discussing stuff about him.)

I've also asked if a T felt comfortable and/or had experience/training in dealing with transference, as that's something that's happened for me.

Note: Regarding the question of "Why did you become a T?" I still haven't gotten my current T to answer that, so don't get too hung up on that question if they don't want to tell you or give some vague answer like "I like helping people."