I'm in no way qualified to render an opinion on the disorder one way or the other, but just from basic social psychology and my own experience, a lot of people, especially 'high self monitors', manifest very different behavior patterns, even thought patterns, depending on the context, or the expectation of the person they interact with. If someone has experienced severe trauma, as in most DID cases, usually chronic trauma from childhood, it makes sense that these discrete self-conceptions might not merge smoothly into one adaptable 'personality', but rather get 'stuck', with the person fearful and unable to regulate them...they have to compartmentalize what would normally be fluid variations in personality because they feel it is somehow not acceptable to 'own' all these aspects 'e.g. shy, rebellious, childlike' and integrate them into a unified self. Maybe indicative of the black/white/all/none thinking characteristic of the BPD that is often comorbid with the disorder. If some people have trouble with affect regulation, why not personality regulation? The 'injured child schema' might get randomly activated at a business meeting, therapy session, whatever. In fact I may have to check out some functional neuroimaging studies on this topic, because I'm sure there are biological correlates for this inability to suppress or activate appropriate parts of the self-concept on command. The point about labeling them with different names, separate entities entirely, in my opinion is just a function of the shame of experiencing these 'foreign' or 'forbidden' aspects of self.
Of course I am just rambling here...I know nothing about the disorder except like 10 minutes from abnormal psychology 🙄.