In the context of Dissociative Identity Disorder (DID), which was previously known as Multiple Personality Disorder (MPD), the answer is yes and no.
In DID, a person experiences the presence of two or more distinct personality states or identities, also known as alters. These alters can have their own unique traits, memories, behaviors, and ways of perceiving the world. When one alter is in control, the individual may have no awareness of the experiences of the other alters.
However, despite the distinctness of these personality states, individuals with DID often have what is referred to as a "host" personality. The host is the primary identity that may be aware of some or all of the other alters and is usually the one seeking treatment or support. The host identity may not always be fully aware of the experiences of the other alters, but they are a part of the overall person.
So, while there are distinct identities (alters) within a person with DID, there is still an overarching common identity that includes all the different parts.
It's essential to remember that DID is a complex and often misunderstood condition. Treatment typically involves therapy aimed at improving communication among alters, resolving underlying trauma, and integrating the identities into a more cohesive whole. Only a qualified mental health professional can properly diagnose and treat DID or any mental health condition.