I feel like the kid almost certainly psychiatric issues, but not schizophrenia or a multiple personality/dissociative identity kind of thing.
Without knowing anything (or at least much) of his history, I'd be looking at disruptive mood dysregulation disorder or intermittent explosive disorder, or a combination of both.
I'd guess that he has a history of severe outbursts (although not necessarily physically violent), and "Jeff" is an attempt on his part to rationalize those moments when he "goes red", i.e., completely loses control, as well as the feelings that he knows lead up to those explosions. The things that Jeff "tells" him and/or compels him to do are just part of his general inner monologue that are closely tied to extreme anger and outbursts. So basically, he's not "making it up", he just doesn't understand what's actually underlying what he's experiencing and why he's experiencing it.
["Rationalize" in the sense of an actual effort to understand them, not exactly to minimize them--I think it's unlikely that he actually has a diagnosis, but would meet the criteria for one].
Ever meet someone who drinks a lot and has an "alter ego" they reference after the fact when they black out? Like, "Oh man, sorry about last night, Henry was definitely out and about, it was wild". Similar to that in the sense of having a somewhat legitimate lack of awareness and control, except in the Henry example it IS an attempt to minimize.
I think it's also important to note that his hatred for Jeff is because he knows he is in trouble for what happened, NOT because Jeff killed someone that he refers to as "mom".
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