Exhibiting two or more distinctive and alternating personalities is a symptom of a(n) * conversion disorder
dissociative identity disorder
obsessive-compulsive disorder
antisocial personality disorder

The exhibition of two or more distinct and alternate personalities is a symptom of a dissociative identity disorder.

Explanation:

Dissociative identity disorder (DID) is a condition of mental disturbance characterized by the presence of two or more personalities in the same person. Usually, the identities associated with the disorder act independently, with one or two of them dominating activity and behavior.

The person affected by DID may experience a loss of memory of his/her own when under the influence of other personalities.  DID can be due to many causes, including depression, post-traumatic stress disorder, borderline personality or drug use.