I had a similar situation with my grandfather from Bisacquino, Giuseppe Mule.The other Giuseppe Mule who came to N.O. with him was his first cousin, both having been named after their paternal grandfather.
I have done research in Bisacquino back to the 1500's using sacramental records. I can tell you for sure that the DiMarco family was there in the Mid 1500's. That name is one that can be easily recognized in the Latin documents.Many time all I can read is the name!!!!!!!!
The earliest DiMarcoI copied a certificate for is the 1815 birth ofa Cyrus born to Calogero and Leonarda Failla.(Baptism record # 439)
Leonarda and Calogerus were married on 2/8/1813.(Marriage record # 222) The names of their parents are also listed.Calogerus's father was Cyrus!!!!!