Yes - that is pretty much a good definition of DID, but we have more than one persona (at least two or more). In my case, I have over 45 or 50. It's hard to keep track. But there are a few alternate personalities (also known as "alters" or "parts" or "insiders") who stand out from the rest, and who come out to handle stressful life situations. The "host" or "main" person is almost always confused and hiding, though she comes out to process and be co-conscious with us once in a while.

The alters have different tasks. Most deal with social stuff - especially the triggering stuff, but some deal with non-social stuff, such as when an alter inside deals with suicidal ideation, or another alter deals with loneliness and depression, or another alter deals with certain memory flashbacks from specific traumas, etc. It's hard for us to be co-conscious when the parts are struggling intensely and feeling some strong emotions.