How to pronounce Griego?

gray-go

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Gree A goh

Paul Griego

American Hispanic

Grego, Greco

Early 13th century during the Venetian Colonization of Euboea, the native Greek families took "Griego" as their surname.

One of the first families of the American Southwest is the Griego Family. Juan and his wife Pascuala Griego arrived in what is now the United States in 1598.
Juan Griego states in the Oñate Muster he was born on the island of Crete in ~1566 and in another document he mentions Negroponte. When Juan Griego was born modern Greece did not exist and Negroponte had fallen under Ottoman rule, an Islamic state is known as Euboea since 1470.
Juan's statement would have most likely been his ethnic identity, Negropontian, and a clue to an earlier ancestor from when it was Negroponte. Both Euboea and Crete are now part of modern Greece but for centuries they were both once part of the Stato da Màr, the Republic of Venice.
When Zuan Griego was born in 1566 (Zuan is the Venetian form of Juan) it was and had been for centuries a Venetian State. Zuan's nationality, culture, language, and ethnic identity were Venetian, a maritime nation that existed for over 1,000 years. At this time the surname "Griego" was a centuries-old proper Venetian surname.