Final answer:
Dissociative Identity Disorder (DID) is the dissociative disorder characterized by a person developing distinct personalities.
Step-by-step explanation:
The dissociative disorder characterized by a person developing one or more distinct personalities is Dissociative Identity Disorder (DID).
DID was previously known as multiple personality disorder, and it is defined as the presence of two or more distinct identities or personality states within an individual.
These alternate identities typically have their own memories, behaviors, and experiences, and they may emerge and take control of the person's behavior at different times.