We do now know nearly enough about the brain to understand what "identity" is for us to speculate on whether a brain transplant would mean losing part of it, let alone actually perform a successful brain transplant in a human.
I'm rather certain that we know enough about brains to confindently say that all the higher functions of the central nervous system quite definitely reside in the brain, and specifically in the neocortex, not in the spinal cord or anywhere else.
What I mean by identity is an understanding of how "you" as a person are formed by phenomena emerging from very complex biological system. For example, I have a very bad feeling in my stomach when I do something I am ashamed of. I'm 99% certain that the neurons in my stomach have little to do with this feeling and it's "all in my head," but we really know for certain how our brain chemistry, our mood, our reactions are shaped by the chemical and hormonal functions of the rest of the body? You are, afterall, combining two separate genetic lines, is there no possibility for a neural rejection like graft-versus-host?
Perhaps the new body does feed back some changes into the brain, but overall we still have a cortex with the original memories, etc as a starting point.
Do you have a link to the larynx transplant paper? That sounds fascinating. I was actually more thinking about very understood practical lines like I know my personality is drastically different (according to friends) on certain medications. With the role even common hormones like testosterone have and the various feedback loops that could come down to the genetics of body cell lines, I can't imagine a person's personality not changing, at least in a time/environment dependent way. Seasonal depressive disorders come to mind, as those seem to have partially somatic causes.
Another interesting question is to what degree does the body (i.e. muscle memory) assist or modify how memories are "pulled up" and processed? Perhaps there will be random unavoidable "corruptions" in the fusing process that result in the signals for stimuli changing (i.e. sensitivity to heat and cold is probably somatic) and the brain pulling up inappropriate emotions or responses?
Is it still your identity if chemical mismatches change your interpretation of your memories over the long term or are you now a hybrid that, due to the transplant, has the extreme fortune of experiencing life and even epistemology in an entirely different way?