I think you’re mistaken, in that it’s naturally the same consciousness but different identities and recognisably different/altered personality states that come in and out in DID. The consciousness itself is always the same and continuous.
From the famous split-brain experiment I would conclude that they don’t share every memory. We are just very good at filling in the blanks, like we can bullshit forever about why that apple happened to be in our hand, even though we have no idea.
