I have now read the article and still propose that they would die if you split someone’s body or just their brains in half.
They put half a brain in a living person.
They also didn’t mention much about different personalities in the article, but different functions (ie, hand attacking a wife and a different hand stopping it).
The closest to different personalities was asking each half a brain (how does that work?) what he wanted to be when he grew up with two different answers, but honestly many people want two differing jobs for different reasons, and so with a brain mashed up like that it would not be surprising.
The half a brain was put with the other half of a brain, which is why they are alive. A person can live with surprisingly little of their brain (I believe as low as 10% is known), but your hypothetical I simply do not believe is possible.