Which mental health disorder involves the presence of two or more distinct personality states?

The presence of two or more distinct personality states is a hallmark feature of Dissociative Identity Disorder (DID). Individuals with DID may experience a fragmentation of their identity, where different personality states or "alters" can have their own names, ages, histories, and characteristics. This fragmentation is often a psychological response to trauma, allowing the person to dissociate from distressing memories or experiences.

In contrast, Bipolar Disorder primarily involves mood swings between manic and depressive episodes, but does not involve the existence of separate identities. Schizophrenia is characterized by symptoms such as delusions, hallucinations, disorganized thinking, and does not involve distinct personality states. Obsessive-Compulsive Disorder involves intrusive thoughts and compulsive behaviors, again unrelated to the development of separate identities or personality states. Thus, Dissociative Identity Disorder is the correct answer as it specifically addresses the phenomenon of multiple distinct identities within an individual.