I'm very close to a teacher myself, she's helpful to me in ways not even my family has, yet I still refer to her by her last name.
It's out of respect.
That can possibly be why Harry refers to him that way, after all Lupin at this point is a teacher first, and a friend of the family second. Referring to him as Remus at this point and even at a later point, would be like referring to Dumbledore as Albus or even any other of the teachers in the same manner.