First idea: Dimidium (Half). This sounds good but the English translation isn't really relevant.
Second idea: Imperium (Control).
The English translation is relevant as it is about the fight for control between the two personalities and the Latin sounds like an English word which people will link to powerful. After thinking about the Imperium name and asking people what they thought, they suggested that it sounds more like a Roman-style film and not the kind of thing we are aiming for.
Third idea: Darker Half
This name is quite powerful in my opinion as it doesn't give away what the film is about too much but indicates the dark, psychological drama genre we are aiming for and sets the tone well. I think if someone asked if I wanted to see a film named 'Darker Half' I would be intrigued as to what it was about.