I have a Gerardo VETROMILE who married a Maria Pasqualina LANZETTA in Bella, Potenza, Basilicata on November 5, 1859
I do not have any children for Gerardo but his parents were Nicola VETROMILE and Livia FERRONE so being his father was a Nicola there is a very good possibility his son was named Nicola (Nicholas)
I only have one Pietro (Peter) VETROMILE in my database and he married a Teresa CELENTANO in 1772. They did have a son named Eugenio born April 11, 1776. I do not follow Eugenio's line forward but his sister Mariangela married a MARGIOTTA.
Hope this helps
Happy New Year!