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There are many variations of the spelling of the name, which comes from the old gaelic O'Duineachea, or something like that. Bottom line is that most peasant Irish were illiterate before 1900 and therefore record keeping priests and bureaucrats merely recorded it the way they wanted.
My grandfather, David Michael Danahy, emigrated from Reallen, Kishkeam, County Cork in 1899 aboard the HMS Majestic to NYC. He had brothers and sisters who preceeded him and settled in Glens Falls, NY., most of whom spelled the name Dennehy. All told, ten of the 11 children of John and Mary (Riordan) Dennehy who survived to adulthood went to America. Most apparently spelled their name Dennehy, although at least three, including my grandfather, went with Danahy. Why the difference is anybody's guess. I have searched in Dublin for birth records under Danahy, Dennehy, and several other variations with no luck. I'm told many records from Cork from the relevant period (c.1870) have been destroyed.
I have visited the family farm, now owned by a cousin, Tadgh Fleming. The original house, built circa 1840, still stands.