To the outside world, it is the same person. On the inside, what if one consciousness ends and another one begins. What if you die each time and another you wakes up. Not you since you are dead. Just another person who will be you going forward. So now, the question is, does anyone even know that is what happens? New you remembers all of that and it is part of their history as a memory. Old you who actually experienced those things is unable to tell everyone that teleportation is deadly.

So I guess, to answer your question, are defined by who you are to the rest of the world or are you defined by the collection of thoughts and actions that make up your experience?

Perhaps the teleported "me" would not be any less "me" than the "me" that wakes up tomorrow.

But, surely, the non-teleported "me" would not be the "me" that got teleported, it would be the "me" that was left behind and destroyed.

Human of Theseus?