The surname Mackay (McKay, Mackay) is the English equivalent of the Gaelic "MacAoidh" from Mac (son) and Aoidh (the genitive of the proper name Aodh). Aodh was a popular Celtic name and is said to be a form of Aed which is translated as "The fiery or impetuous one".
With the passing of time, the spelling of "MacAoidh" has taken many forms including Iye, Y, Aytho, MacIye, Makky, Macky, Maky, McKye, McKeye, Mackie, Mackey, McKy, McAy, McCei, MacCay, Mackee, Makgie, Ison, Eason, Easson, and many others. The name MacIsaac is said to be a corruption of MacIye.
Clan Morgan, the old name for Clan Mackay, may be derived from the Moray connection of the clan. Earliest reference to Clan Morgan is found in the "Book of Deer," where the toisheach of the clan is so described. Sir Robert Gordon tells us that the clan was termed Clan-Vic- Morgan from one Morgan who flourished in the fourteenth century.
[From: "The Clan Mackay", by Margaret O. MacDougall]