I assumed that our letter-based code names don't have anything to do with Wammy's House seeing as our characters aren't supposed to know each other. As such, it shouldn't matter at all what our code letters are whether it's L or N.

It's probably to keep identities secret as an anonymous think tank so that no one detective has sway over the others or even as a scare tactic against Kira. Like "The original was beaten by just L, and we've got the whole damn alphabet on your butt."