Look, the fact that you just said that Sunny is in White Space and Omori is out adventuring already is a contradiction. The fact that people with DID have internal headspaces is true, but no matter what, there is always at least one alter using the body at a time. The fact that Sunny doesn't switch while he is conscious, wake up with Omori fronting, means that this is not DID. One of them would have to be in the mental world and one would have to be in the body, and Omori only shows while Sunny is asleep. People with DID also experince an amnesiac barrier, but Sunny does not experince this. We know this becuase Sunny knows what he did, and wont forget it, which is why he becomes a shut in. If there was an amnesiac barrier Sunny would be able to continue with normal life (sort of) or Omori would continue the normal life for him, neither of which happens in the game, and this is proven by Kel saying that Sunny never goes outside anymore.