It was true. 'Moll' was used in the 1920's and 1930's as a slang term for a gangster's girlfriend and less widely, for flappers and such 'types'.
In the 1700-1800's Molly and Moll were used literarily as common names of housemaids and domestics. There was a famous London beauty named Molly Mog (1699-1766) and JohnGay wrote 'Fair Maid of the Inn' about her. Then in Tom Jones (1749), Henry Fielding wrote of the maid Molly. Daniel DeFoe's Moll Flanders in 1722 also helped it's lower-class image and MollieMalone in 'Cockles and Mussels' gave it's Irish associations a boost (it's not, it's English).
It's nothing major to worry about now. In the 1800's Abigail was also more lady's maid than Lady ;o) And Mary itself was more widespread in the working and impoverished classes than the elite of the time. It all rolls on and all three are firmly yuppie today.