It's slang here for idiot, twit, etc: "I (did something idiotic) and I felt like a right nelly" so it's always sounded quite comical as a name to me, and I definitely wouldn't use it as a stand-alone name.
Not sure when the slang use originated - my great-grandmother, her eldest daughter and a couple of cousins were all called
Nell and
Nellie, short for
Helena - and it may be on its way out, as
Nelly and
Nellie both reappeared as stand-alone names in the last two England & Wales charts. But I prefer
Nell by miles, and only as an nn.