There are at least two bands by the name Molly.

The first, doesn't exist anymore, but they were a great Swedish band playing something along the lines of; old irish rebel songs, ska, punk & folk.

The second was a power pop band from Grand Rapids, Michigan most recently releasing an album entitled "The Finger" on Idol Records and prior to that the album "SeXXX Sells" on Sid Flips Records and a self-titled, self-released EP.