There's no such thing as a "head transplant". The person receiving the transplant is the one whose head it is. The transplant they receive is the rest of the body. Therefore, "full body transplant" is a more accurate term.
Respectfully, I don't think you or anyone else alive right now actually knows how this would go down. The amount of interactions between organs, central nervous system, endocrine system, and brain means I'm not sure anybody involved would remain "them"