I know, that was my point: it's NOT DID, rather
Gollum's symptoms more align with Schizophrenia, as your definition clearly matches.
There's one problem with single symptoms, probably often even combinations of them, that they can appear across a whole spectrum of ailments, often both physical and psychological. Diagnosing any one ailment can be tricky.
The bit about Gollum speaking to himself, or as it is portrayed in both book and film, the
Sméagol - Gollum "debate", might speak against both schizophrenia
and DID. But I'm not on firm ground here, and the professionals might give me quite a dose of





.
But as I remember it, the hearing of voices afflicting the schizophrenic does
not include the schizophrenic's
own voice. They might enter into a dialogue with the
other voices, not sure about that.
As to DID, in at least one variant of it, the multiple personalities
do not know about each other, at least not first-hand. They might be told about the "others" by other people who have witnessed it, or perhaps by therapists (these might even record videos of the "others", again no idea of they do). So that would seem to exclude any possible "dialogue".