"Fahy" appears as an element in many Irish placenames, meaning a green or level grassy place, and this may have something to do with the occasional anglicisation of O Fathaigh as Green. Fahysvillage in Athenry parish certainly records the family name, however.
In 1890 there were 114 births of the name, with more than half of these in Co. Galway, and particular concentrations also in the adjoining counties of Mayo and Tipperary. As well as Fahy, Green has been used as an anglicisation of a number of other Irish originals, including O Grianain, Mac Glasain and Mac Giolla Ghlais, either through a phonetic resemblance or a supposed connection with glas, meaning the colour green. For this reason, and of course because many English settlers bore the name, it is now very widespread throughout the country.
Father Anthony Fahy (1805-1871) became famous in his adopted country, Argentina. The fahy Institute there is named for him.
.Francis Fahy (1880-1945) played a prominent role in the War of Independence and became ceann comhairle (speaker) of the Irish parliament Dail Eireann after independence.
David Greene (1915-1981) was a senior professor in the School of Celtic Studies in the Dublin Institute for Advanced Studies from 1967 to 1981 and was well known in Irish life for the rigour and vigour of Hs views.