A moon monkey is the nickname for anyone who's surname is Muloolly or Mullooly or any other spelling I can't think of right now. Instead of having to remember what their name is and how to spell it, just call them Moon-Monkey
Girl A: That Nicola Moon-Monkey has had a baby you know?
Girl B: Oh yes, what has she called it?
Girl A: Maia Pearl Moon-Monkey
Girl B: How nice!