Aristocrat pet names can be very peculiar. Horace Walpole's pet name for his friend George Montague's sister Henrietta (d.1755) was "Hounsibella." In fact, from his letters, we know Horace had already dubbed her that by 1746 which is right around the time he claimed he first heard the song he sent to Percy. This is further confirmation that "Lady Hounsibelle and Lord Lovel" was indeed around in the early 1700's. The burlesque LL seems to have been a special favorite of HW.

While, aristocrats have certainly used nicknames. I think it is more of a class connotation that goes with Nancy, a commoness or even a certain bawdiness. There are those who would agree:

Nancy 

I think authors generally put thought into the names of their characters. Why did Dickens chose Nancy?

I'm sure you know what a "Nancy boy" is right? Why Nancy? Why not some other name? There seems to be some suggestion of lewdness attached to it.

And then there's that line from "Rocky Racoon":

"Her name was McGill, she called herself Lill, but everyone knew her as Nancy."

Something about that name puts it on the lower end of the social spectrum, more so in yesteryear than nowadays (because we are so caught up now in token egalitarianism I suppose).