There was a Clan-Aedha (Aodha) in Ireland c.1172 and whom well have been there for centuries, and then perhaps written or recorded by the English as Adare (as in Castle Adare). refer http://www.ucc.ie/celt/online/T000003/text001.htmlhttp://www.ucc.ie/celt/online/T000003/text001.html
M1172.6 refers to the clan as Clann-Aodhe
M1173.7 refers to the clan as Clann-Aedha
The Kennedy family in Scotland whom the Adairs married into may have originated from the O'Kennedy, Lord of Ormond shown on the same page(M1180.9), but I have not checked out their origins. This perhaps may account for the story of the Kennedy/Kenzie/Adair story of origins. There was a Kennedze who slew a White Knight.