Everybody's experience is different. It is definitely possible to have parts that have no names. Sometimes parts may name themselves, name each other, or be named by a host part. Sometimes parts will all identify with the same name, but may identify as Three (years old,) Twelve, Nineteen, etc. Sometimes parts will have descriptive names, like The Baby, The Angry Man, the Protective Woman, The Professional, etc. Sometimes parts do not have any sort of true, developed personality of their own. They may exist only to contain one particular memory, or to do one particular task. Outside of those duties, they have no other interactions with other parts or the outside world, and have therefore not developed into what is typically thought of as a separate personality.

I read a really awesome book that was very meaningful to me. It is a personal account of the struggles and healing process of someone with DID. It's called The Sum of My Parts, by Olga Trujillo. The first part of the book contains some very graphic scenes of abuse, so you may want to skim, or skip altogether that portion of the book. At the beginning of the book it warns of this, and makes a suggestion of what chapter to start on in order to skip the more triggering portion. The second half chronicles her understanding of the way her mind works, the ways that her parts helped her, and her integration. She explained and described it all in a very different way than I have heard DID described before.

Sometimes I think people diagnosed with DID try to mold themselves into their idea of what DID is "supposed" to be, but there really isn't any "supposed" to. Whatever you did to survive was the right thing for your mind to do. The fact that you're still here is the proof.