'Nancy' is of course just a familiar form of Ann, just as Molly/Polly [the commonest alternatives] are of Mary: probably the two commonest female names at the time.   Roy Palmer writes somewhere in one of his collections [this is from memory], to the effect: "Nancy and Polly, William and Jack — these are rather representative types - a sort of archetype - rather than to be regarded as actual people".

I would generally get a laugh from not-all-that-folkie audiences with some such intro-formula as, "It was a rule that any girl that wanted a sailor to fancy her had to be called Nancy; at least, I used to think so, till my wife came up with an alternative theory — that there was just this one girl, who travelled all round the country, from seaport to seaport, Yarmouth to Weymouth to Liverpool to London... Anyhow, here's the song."