From "The Straight Dope":
Never underestimate human ingenuity. Margaret has spawned an amazing variety of names, some of which you wouldn't connect with the original in a million years. For example: Margot, Marguerita, Rita (!), Greta, Gretel, Gretchen, Marjorie (originally Margery), Margie, Maggie, Madge, May, Maisie, Daisy (!!), Maidie, Meg, and Mog. As for Peg, one historian writes, "the nicknames Mog and Meg later gave rise to the rhymed forms Pog(gy) and Peg(gy)." Can't say as I know a lot of Poggies, and can't say as I want to. But you see how Grandma Margaret wound up with Peg.