I think the correct answer is that the mind is one, but the consciousness are two.
How does that work? If there are two consciousness-es with different believes, desires, opinions, emotions, etc, what is the mind and what does it do?
I think the mind goes far more deep than just believes, desires, opinions, emotions and all that, I think it even goes more deep than just mere consciousness. I think this in part comes from a western way of thinking (oriental philosophies may disagree. I've heard buddhist have the concept called Anatta, which is basically the no-self concept).
The general idea of how this may work is upon realization that the self is not any of the things listed above. For example, you are thinking, but you are not the thinking. You are in pain, but you are no the same as the pain, or you can be happy but you are not exactly the same as happiness. So it seems you are not any of those individual things, but you are the "holder" (temporarily) of this things. It doesn't seem that you are neither the fussion of this things, since you can be knocked out with anesthesia and lose every and all of this things, including consciousness, but upon waking up you are still you. If you were just consciousness, it would seem that when you were knocked out, you dissapeared entirely (since no consciousness remained), and upon waking up a copy of you took your place, which doesn't seem to be the case.
So, if you are none of those things, ¿what are you? I think a great part of that lies in the subconscious, which as I see it, guide many aspects of our lifes, the so-called repressed memories, subliminal perception and other phenomenon (which sometimes can mix with the consciousness aspect like in the tip-of-the-tounge effect).
If you split the brain, each part takes a part of this mind (a part of the memories, and neural networks that we don't use for awareness) gets attached with a new consciousness, and another half gets to stay with the other consciousness, but since they both have half the mind, I think the correct answer is that they both, in sum make one mind, that gets two consciousnessess.