Why was multiple personality disorder renamed?

Dissociative Identity Disorder (DID) also known as Multiple Personality Disorder (MPD) was changed to such because as people have become more aware of what this disorder truly means - there have been some major changes. 

When you hear the word personality you reflect upon the individual's actions, behavior, mood, etc. A patient with DID lacks one way of acting, they circulate throughout multiple personalities. 

A reason for changing this is to highlight that the problem is not multiple personalities, it's the fact they do not possess a unified one.

Hope this helps!