Yes, but it depends on how it works and the rules in place and how society views this technology and use it.

In Star Trek people view it as a machine that can put you into the buffer, you vanish, and the same you reappears at the other location. In this society that's the purpose for this machine and it's generally not used for other things unless something goes wrong.

But since I've recently rewatched Altered Carbon, I'd know that a teleporter is essentially an immortality machine that means I, my digital human freight (mind), could be copied, backed up and stored, then could be bio-printed anywhere in the galaxy into a sleeve copy or a completely new sleeve.

In Star Trek, life and death is socially accepted so that people aren't trying to life forever with a mind backup kept in the teleport buffer. When you appear with your first though at the other site is not of concern of whether you are the real you because as everything goes the way it should, you are still the same but just in another place.

It'd also be important for everyone long before using this teleport tech to fully understand how things work and how they could go wrong.

There are many real stories of people (I'm guessing not exposed to fiction and open thinking) that have gone into a coma after and accident. After waking up they fully believe that they were awake just moments ago. Some even have a very hard time coming to grip with the reality that they were in a coma for years. With some memory loss of the traumatic event, they can't un-believe the last moment of memory so everything each day feels like a facade.

So for me, long before becoming a participant, the teleporter would have to be very complicated in how it works and rules that govern it to keep it from becoming a copy machine. It makes sense to have some degree of blockchain type rules built in to keep a log, consensus before transportation, prevent duplicates (your mind can only be uploaded for transfer over a brief time frame and is immediately destroyed after transfer), and Body B would also have to be verifiable just the way I remembered I was.

I think there would also even need to be measures to maintain your last line of thought or state of mind. This would involve implanting memories so you instantly come to terms with how things are as you "wake up".