"Lily Evans," she replied as she shook the offered hand. Her granddaughter made such a fuss about distinguishing themselves that she was starting to include her last name in her introductions. She, however, felt no compulsion to add any notions of clarifying beyond that.
She was moderately amused that her magic had been referred to as nifty, and she reasoned Pepper must be familiar with magic -- or had been here for a while.
"Have you been here long?" She inquired. Well, it followed her particular train of thought, and it was one of the standard 'I just met you' questions -- what's your name, have you been here long, when are you from, and so on and so forth.