I applaud your openness and sensitivity, too. I've had about a dozen therapists (when i was misdiagnosed and psychiatry didn't recognize DID.) I would try not to mention other T's any more than necessary, but sometimes is necessary when a former T messed me up some way that's showing up in the current relationship with T now. I feel petty and like a gossip...two things I don't allow myself to be. But some things need to be discussed when it's important to progress with current T. I know it's hard to decide.
Just a bright note about changing therapists... I'm doing really good with current T and believe I will make it to full recovery this time. It's discouraging to some folks to hear me say I've been through many therapists. But it only takes one...the right one, and it took several changes to get to the right fit. I think you did the right thing for yourself because of your past posts about severe difficulties with your first T.