"I can give you my number," Lancelot offers, and he digs for his phone -- swipes the screen and looks up at Arthur expectantly. It seems easiest, and he isn't particularly bothered by Arthur having it. Lancelot has nothing in particular he wants to hide, and short of irritating him with a lot of phone-calls he can't imagine Arthur doing a lot of damage with it, after all. "It will help if I had a name of some sort to call you, too."

After all. Arthur has seen his ID -- knows his name, but hasn't given Lancelot one at all. Maybe he's careful about these sort of things, he isn't sure, but he isn't particularly bothered if he's given an alias of sorts so long as he has something.