Dreams can make dream characters appear as if they have a mind of their own but they don't.
Not meaning to go off topic, but remember DreamCafe, I'd say we still know very little of the nature of dreams, as the same is with the origin of consciousness. For all we know we could all be DCs in a persistent world inside of someones head. That'd be so crazy lolol. I'm not saying all DCs have their own consciousness, but there are a few from time to time that surprise me and they don't seem to be apart of me in general. Some of the DCs I have encountered I have had perfect conversations with; everything they said made perfect sense and I swear they knew things that I've never even come across before. But then again, that brings me to the topic of astral projection so I won't get started on that haha.

One things for sure, there is a definite reason our mind is often compared to the universe.