In history of the Mayo name has been given as May, Maye, Mayeo, Mayow, Maiewe, Mayhowe, Mayhue, Mayhew, and other variations. It is supposed to have originated in County Mayo, Ireland, although it is not a common name in Ireland.
Details can be found in the following book:
"A genealogical account of the Mayo and Elton families of the counties of Wilts and Hereford; with an appendix, containing genealogies, for the most part not hitherto published, of certain families allied by marriage to the family of Mayo", by Mayo, Charles Herbert, 1845-1929, published 1882.
Read the book online at Archive.org.