DID (Dissociative Identity Disorder) and MPD (Multiple Personality Disorder) are psychiatric diagnoses used to describe plurality, most frequently trauma-based systems. DID is the current term; MPD was outmoded a few decades ago.
DID is said to be caused when severe trauma results in a failure to integrate memories, thoughts, actions and beliefs into a core personality. The trauma associated with the memories and thoughts eventually develop into a separate identity with it's own pattern of behavior and personality. Dissociation becomes a defense mechanism to avoid traumatic events and memories, and over time can become a hindrance.
Some plurals may associate with the term and identify with it, however others may not, often due to believing that trauma is not the cause of their system.