Dissociative Identity Disorder (DID) was previously known as Multiple Personality Disorder (MPD) in the Diagnostic and Statistical Manual of Mental Disorders (DSM) up until its fourth edition (DSM-IV). The term "Multiple Personality Disorder" was used to describe the condition where individuals exhibited multiple distinct identities or personality states within themselves.
However, in 1994, with the release of the DSM-IV, the name of the disorder was changed to Dissociative Identity Disorder (DID) to better reflect the nature of the condition as a dissociative disorder. The change was made to emphasize the role of dissociation as a central feature of the condition, highlighting the disruptions in memory, identity, consciousness, and perception that individuals with DID experience.
So, technically, there are no examples of a person being diagnosed with both DID and MPD, as they refer to the same condition, but under different names at different times in the history of the DSM. Today, the correct and current term for the condition is Dissociative Identity Disorder (DID).