I had a great-aunt named Mildred who was always called Minnie. Also, Minnie Driver's real name is Amelia, her sister couldn't pronounce it so she ended up as Minnie.
Other things it might be short for:
Melinda
Miranda
Minna
Wilhelmina
Jasmine? Jessamine?
Jemima?
Mary
Margaret
Marlene/Marlena
Monica?
Miriam?
Marian?
With Minerva, you'd be lucky if she ended up Minnie. She'd probably get called Nervie at least a few times.