I think many people here in PC would be happier without or with less attachment to their therapist

Didn't the other T suggest some other kind of dissociative disorder? I think it is a spectrum, much like many other mental health diagnoses. The classifications are for the sake of description, but I don't think any two people with the same formal mental health diagnosis experience them in an identical way and with the same severity and these things often even fluctuate over time for one person. This is part of the reason it is so challenging to treat mental health issues and they change and shuffle the diagnostic terms because, clearly, these things are not so well-defined.

Maybe it is not that important what it is called and more constructive to focus on your actual challenges in therapy? There are people here on PC who talk about having issues with dissociation but do not experience losing time and a strong disconnection, more like different (and often conflicting) motivations, desires, feelings, even behaviors. Maybe what would help is to just focus on the process and engage in a treatment plan - see what happens, perhaps you would get more comfortable with a diagnosis over time as you get to know these different motivations, forces, parts, alters... call them whatever.

This skepticism and hesitation of yours reminds me a bit of something I have seen in people who struggle with addictions many times. They often refuse the label because there is so much stigma associated with it and also because they don't fully want to give up whatever habit they have. I am personally one that finds diagnoses useful and don't mind at all, but often say it does not matter what we call it - is it a problem or not? Do you want to work on it or not? If yes, focus on the work. If not, why think about it and spend time investigating it?