So essentially, you're no longer a biological human after becoming a cyborg. I think that makes sense. That being said however, what makes you feel human, your memories and emotions and free thought, would still remain. You may not be considered a human by other people, but you yourself would still remain a person.
Exaclty yes, that had been my point all along. If we are acknowledging the possibilty of intelligent life not necessarily rooted in humans then the nature of what we consider to be an intelligent, self-aware feeling creature changes right? An human and a supposed cyborg are both people in the sense that they are intelligent, self-aware, feeling etc but only one is a human being where-as the other is now a cyborg.