I have more experience with this than I want to admit to. What you describe is very typical of what a lot of Christians would call demonic possession.
However, when you add to it that many of these people have MPD (Multiple Personality Disorder) issues, it can muddy the water. The Enemy likes to hide within or behind different personalities within the same mind.
Also, despite what the Church tells you, the name of "Jesus" is not what makes these demons leave, it is Natural law that makes the go. "Rebuke the Enemy and he will flee from you" is all that is needed.
But telling something to leave is not always an easy thing to do when someone has allowed or invited a dark spirit into their lives.
Yes, praying for someone under the influence of a dark spirit is probably helpful, but quoting a bunch of Bible verses at a demon is going to be next to worthless. They will just laugh at you, which was some of my earlier experiences with so-called "spiritual warfare".
My biggest beef with Christians "casting out demons" in some ridiculous "exorcism" is our lack of understanding of these dark spirits. The Church has not helped with all of its "exorcism" nonsense either.
The best thing to do for someone behaving irrationally under the influence of a dark spirit is to love them and annoy the demon to the point where it gets bored and leaves (stops manifesting). Then it's up to the "host" to rebuke the thing and get rid of it. And that's not always an easy thing to do with someone who is MPD.
My wife has a couple of books on this topic about to be republished on Amazon. Both are exceptional reads and really take the "spookiness" out of the whole issue, which is what we need more of. But it's always weird trying to understand something we cannot see.