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.
Interesting perspective, do you believe that every moment there are new "yous" coming into this world? Like I am not the same me when I am angry, I am also not the same me that I was 5 minuites ago. In this case would you believe the teleporter to be a transportation device?
You are a new you when you wake up in the morning, when you have coffee, when you eat. Yes. I think so, adding new cells and loosing others.
The conclusion is the teleporter is not a transportation device, it destroys you and recreates someone (extremely similar to you) in the alternate place. It's only when this person gets there and someone says "Hey Alex!" that continuity is formed.