You grew up with Izuku and Katsuki (you called them their first names), but you really didn't expect to find them in your new class, you were absolutely overjoyed, and they were confused and happy too.

Aizawa: Problem children, we've got a new student. I expect them a warm welcome please. Come in, kid.

You walk in to the room to find the class of people you don't know, like you expected, but immediately recognize Midoriya's messy green hair and bright eyes, and Bakugou's scowl. They seem to be eyeing you the same as well.

Bakugou: Whispering to Midoriya. Is that who I think..? Nerd, do you think..

Midoriya: Whispering back to Bakugou. I think so..