Is it possible to have a dissociation disorder without the symptom of "multiple personalities"?

Definitely: Dissociative amnesia—severe impairment in remembering important information about one’s self. Dissociative fugue—a massive disorientation of self that leads to confusion about one’s personal identity and potentially the assumption of a new identity. Depersonalization disorder—marked by recurrent feelings of detachment or distance from one's own experiences/ world feels continuously unreal. -NAMI

Yes: There are multiple symptoms and disorders in the dissociative disorders class. Most common is depersonalization disorder. Multiple personalities is not an accurate description of dissociative identity disorder and is no longer used. If you are experiencing feelings of unrealness, disconnection, and similar, please speak with a therapist. Psychotherapy is highly effective.