What kind of pepper am I growing?
Mis-tagging happens more than you would think. Depending on where you got the plant, they could tell you what the most likely variety it could be. It's hard to tell the exact variety. It could be a Scotch Bonnet or a 7 pod, or one of several others. I'm not familiar with Carolina Reapers, but from the pictures I've seen, the fruit does not match what you have. That said, it could be that the fruit change shape some as they mature.
Sorry I can't give you a more specific answer.