Indeed. The transporter is a way of travel, not a copy machine. If it were you could tie it in with the replicator and create people.
They more or less do that at the end of Lonely Among Us.
But yeah, it's one of those situations where canon's all over the place.
Personally, I can't think of any way the transporter could
work that wouldn't mean killing the transportee and recreating them. But we can dismiss that easily enough: If the transporter killed you every time you used it, no-one would use it. Just about everybody uses it, so we can assume it doesn't kill you.
There would be no way to know! You would realize it as you died, then your clone would emerge, none the wiser, thinking that it IS you and always has been.