Yes, sometimes the personality splinters as a form of dissociation, sometimes it's just a manifestation of an underlying neurological disorder.
A personality is not like a 'ghost' in the machine, however, it's a construct of the brain, for the subjective self, to flesh out the idea of self an allow the self to interact with others and appraise its own actions. You can see from the last sentence how much room there is for situations to create a 'personality' which 'self-rejects' or is hugely inappropriate in certain circumstances: so the brain creates a few of them.
Multiple personality disorder is commonly referred to as 'schizophrenia' and vice versa by the unwitting. Schizophrenia is indeed a splitting of the mind, but in a way that it fails to integrate various cues about reality. This is different from the personality itself splitting.