My T uses the term "self states."
When I first became aware that there are different parts of myself I was terrified. I called T in a complete panic. Like Sunny's T, my T said that it is accepted that most people have these varying parts.
I do not have DID, but I have lost time.
I am currently sharing time with my 8-year old self. She is a very wounded self state, who spent an inordinate amount of time fantasizing so she wouldn't have to face her lonely, scary life. T is teaching her good self care.
Good luck to you.