Minnie
Minnie was wildly popular at the turn of the last century--it was a Top 10 name in the 1880s-- but is completely obscure today. Blame Mickey's girlfriend. Though it's possible that the up and coming trend toward old-fashioned nickname-names -- think Maisie, Mamie, Millie -- may give Minnie (all on its own, not as a short form of anything) a new moment in the sun. Minnie Driver (born Amelia) has given it some modern celeb cred.
Minnie can really be short for just about any M name (and some non-M names as well), including Mary and Margaret.

