The explanation for the origin of the name Cunha follows:
This first Conde da Cunha had two sons. The first son became the second Earl and established his family at Viana do Castelo. The second son led a military life and ended living in Lisbon where he founded another important branch of the family. Both branches produced along the centuries some of the most important persons in the history of Portugal.
There was a Cunha castle, near Barcelos (north part of Portugal), which gave its name to the village. With the advent of the new Portuguese census regulations of the 18th century, everyone had to take a surname; until then only nobles had a family name. Many people working for a certain family took their name and others took the name of his or her home village. The large majority of today's Cunhas descend from these people who took the name. To this day, direct descendants of the first Earl of Cunha live in Portugal.
The majority of da Cunhas in Graciosa are descended from the Captain Donatary of Graciosa, Pedro Correia da Cunha, who obtained the captaincy in 1474. Pedro himself was the "..nephew of Joao Pereira da Cunha, one of the Twelve of England. Joao Pereira da Cunha had been one of Portugal's greatest knights in the 1390 tourney." (James Guill, "A History of the Azores Islands," p. 158). Mr. Guill also shows a photograph of the home of Pedro Correia da Cunha in Santa Cruz, the capital of Graciosa, which has been restored.