DID IS a particular kind of dissociative disorder. There aren't further specifiers on that (unless it is a severity specifier having to do with the number of alters - though I'm not sure that is DSM compared with particular clinicians theories).

ICD doesn't have a dx category for DID so he would get something different out of there... NOS something or other... It is kinda lumped with Gansers Syndrome...

Though...

It might be that he is better regarded as having MPD (no longer appears in the DSM). Interesting issues are brought up when it comes to dxing characters in fiction or in history...

Not terribly supportive of it myself...