Two possible reasons in my book:
One: The only thing I know to have two personalities is zetsu. Madara is known to have hashi dna which is why zetsu. So maybe it is something to do with that. Or as you said maybe obito's body as the host and could give his personality.
Two: Uchiha's are good liars/actors look how itachi acted as if he was pure evil and had no emotions after the massacre. Even so he was catch crying that time he thought sasuke was probably dead probably because he failed. Tobi wears a mask that means he can also hide all facial expressions.
Also we need to realise that this is a anime and it's just what kishi wrote know way someone could act that goofy but really be that serious.
