My Brun family changed their name to Brunn in the US; they are also from Andreis, Friuli region. My ggrandfather's name was Luigi (Louis) Brunn, his father's name was Giovanni (John) Brun, and his father's name is uncertain, but may have been Antonio.
The Brunns in my family eventually settled in Hazleton, PA; Louis married a Maria Rosello, whose mother and father, Rocco and Carmela Minuto Rosello, also came from Italy, and we think they emmigrated from Brindisi, but were factually rom Northern Italy, too.
Some of our Brunn family lived in Little Italy, in NYC; Rev. Joseph Brunn, of the Broome Street Tabernacle, is a relation.
Is there a connection with your Brun family?