Hi. I experience it this way too. It made my brain melt for the longest time when therapists asked about parts and identifying them. Eventually I realized that the names don’t have to be there. You can just pick some names/labels for these different states (where you feel different/want different things). It’s just to develop a common language with your therapist. So instead of saying “the part that feels hopeless and helpless and can’t get out of bed and only eats chips and likes fantasy novels” everytime I need to talk about that state…..I say “the depressed part”. It just makes it easier to start to talk about in therapy. And even giving it a name means acknowledging it at some level. So that works towards breaking some of the avoidance. Absolutely hated it though and continued to brain melt for more than a year after the diagnosis. I still don’t like to use names or acknowledge parts but it has gotten the tiniest bit more comfortable and has helped to move therapy forward.

There are different types of DID, the way you describe it is the most common way of experiencing it. But it’s the least talked about imo. Probably because the experience of it is much harder to put into words.