I was surprised to hear that the song is called La Danza? Would like more info. To the best of my knowledge it was called "Lazy Mary" on Lou Monte's recording, and it called "C'e 'na Luna Mmiezzo Mare" in the area around Naples. I don't think it's specific to Naples though.

Does anyone know whether it was originally published as sheet music? And when? If so, then it would have an "official" name. A lot of "traditional" Neapolitan songs such as O Sole Mio are basically parlor songs, written and published in Italy in the late 19th century. Is this one of them?