He used to pal around with James and Sirius who used to bully Snape.

What I mean is, there was intra-Marauder tweaking as well, and Remus probably stopped thinking about it. (Peter didn't, obviously.) If they're true-to-form spoiled fratboys, Sirius and James probably had more disgusting things to call each other than Prongs and Padfoot, and we know Sirius's cavalier attitude toward full moons with Remus. To Remus, all that is wrapped up in what he would consider a good and warm relationship. So I don't think he'd necessarily think that tweaking Severus's ego was in direction opposition to being friendly.