L is a code name, but it's also an in-between name, a placeholder while he figures things out.
His new name will start with an L, he knows. He has always liked the symmetry of his initials, even while hating his name.
He keeps a list of the possibilities, writing new names down as he thinks of them, crossing them off when they don't quite fit.
L is a good name until then. He likes the feel of it in his mouth. Nothing else feels quite right yet.
Someday he will settle down, but for now he is just L.