I don't see why there can't be two Ls, perhaps to confuse kira which is the real one? Of course it's painfully obvious to our characters this L couldn't be the previous one, but other people wouldn't know who's who.

I'm assuming our character letters are just fake and don't hold any real meaning.

As for Near taking the letter L, it was as you say part of keeping L's death a secret, but I truly don't know for sure if you automatically get the "rank" of L or if he just took the letter only for that reason. I thought it was a rank.