Genay is of American origin, derived from French 'Jean', meaning 'graced by God'. It's a unisex name but more commonly used for females. In the United States, it gained popularity in the mid-20th century and has since maintained steady use.
"Between 1980 and 1991, the name Genay was given to a total of 32 newborns each year, with peaks at 9 births in 1989."