...I wouldn't use the NN Mim. Reminds me too much of Mad Madame Mim from "The Sword in the Stone"; great character, but maybe not the type of association you'd want for a little girl.
I'd go with Miri as a NN, or Mira. I know you already have a niece named Mira, though, so that's out. Maybe Minnie could work?
I like Margaret because it's a classic, but it's a little dowdy to me. I keep thinking of dumpy, middle-aged women with gray hair and too many cats. :P