The name D'Amico can be traced back to the 13 century and is believed to be a patronymical name as in 'from Amico' (son of Amico), agiven name that shows up from time to time.
I have recieved a history of the family name as part of my memership in the National Italian American Foundation and can trace it from th 1200s from northern Italy to Sicily.
I also received a copy of The World of D'Amicos book which attributes the origins of the name to similar circumstances.
There is a coat of arms and crest attributed to the D'Amico name and we are cited in Spreti's Enciclopedia Storico-Nobilare Italiana.
My family is from Napels and we were looking for a connection to the Barroness Di Castel Cicciano. (As you can see the Baroness was a D'Amico but related to the Amico family of Malta-- it was just a thought.) We also had prosperity in our family, and were told of some remote nobility.
I would be interested in cross checking our ancestors.
My grandfather Ernesto was from Napels, born there in 1877, had two brothers and one sister. One brother, Giovanni came to America and setteled in Queens NY but I havge no contact with any of his children.
My great grandfather was Alberto (I believe), and his wife, my great grandmother was a Di Pasquale (I'm not certian of the spelling).
Hope this was a help. I would like to hear any cross connections in your family research.