I was discussing this with my friends yesterday by the pool.
My conclusion is slightly Buddhist leaning. 'You' means different things when consciousness gets involved. I am a different person when I am angry, than when I am happy. I think it would be the same with trans-humanism.

It would mean in this situation that the recreated (teleported/upgraded) you, would not be you. Much like in The Prestige or respawning in a game. The congruent 'you' is a construct of your surroundings. It would be just as tough to change the definition as to change one's own name.

My two cents.