I think the name calling here is more sour grapes than anything else. I intend to speak to his big brothers about the idea of building themselves up instead of tearing other people down, and about the possible consequences of anything that could be seen as bullying in today's world.
I'd like to say I'm torn on spanking Gavin. After all, he's a really cutey, and he hasn't had anything but birthday spankings in a close to two years. Still, the honest truth is I'm not terribly tempted.
I might consider getting his bottom bared and getting his paddle out, then having a discussion with him. For one thing, while I don't want him to make a habit of lying, it's not like his brothers are around all the time. The next time his brothers tease him about this, he could simply reply, "you guys aren't around all the time," or, better yet, "you're just jealous because I don't get caught."
I think that kind of evasion would stand him better than a spanking.
And if he does decide to go earn one, then he'll get the same thing his brothers would.