First off, you could've simply typed your name into the search box on the main page of Behind the Name. And secondly, you should go to the other board for opinions on the name Molly.
MOLLY f English Pronounced: MAWL-ee Pet form of MARY
MARY f English, Biblical Pronounced: MER-ee Usual English form of Maria, which was the Latin form of the New Testament Greek names Mariam or Maria (the spellings are interchangeable), which were from the Hebrew name Miriam. The meaning is not known for certain, but there are several theories including "sea of bitterness", "rebelliousness", and "wished for child". However it was most likely originally an Egyptian name, perhaps derived in part from mry "beloved" or mr "love". This is the name of several New Testament characters, most importantly Mary the virgin mother of Jesus, and MaryMagdalene. Two queens of England have had this name, as well as a Queen of Scotland, MaryQueen of Scots.