Molly has been used as a stand-alone pet form of Mary since the Middle Ages, and has been consistently popular as an independent name in the US over the past several decades, still in the Top 100, and in the Top 40 in most of the English-speaking world.
Likeable and down-to-earth, mild yet saucy, Molly has a distinctly Irish feel as well, with such Gaelic associations as Sweet Molly Malone and the martyred reformers known as the Molly Maguires. In the Jewish culture, Molly Goldberg was an early television personality.
Other references include the Revolutionary War heroine Molly Pitcher and the Molly Bloom character in James Joyce's Ulysses, as well as characters in novels by Fielding, Hardy, George Eliot, Dickens and Thackeray. More recently, "Good Golly, Miss Molly" was a Little Richard hit and Molly Ringwald a celebrity bearer.