Book "Surnames of Scotland", The New York Public Library.page 6. ADAIR. "It is a fact that Thomas Edzear or Odeir had a charter of the lands of Kildonan in the Tynes of Galloway from (King) Robert I." (see my entry for Great Seal of Scotland 1306-1424). From the (King Robert I) the Bruce, also various parties of the same patronymic had grants of land in Dumphries. Richard dictus Edger (Edger, Edzar, Edzer, Edzear), for example, had a charter of the "place of Seneschar" (Sanquhar, Upper Nithsdale) "and half the barony thereof" (this is also in the book Great Seal of Scotland which I have copied).
"The name (may be) simply a form of Edgar, the progenitor being probably Edgar, son of Duvenald, a leader at the Battle of the Standard (1138), grandson of Donegal of MORTON CASTLE, a descendant of whom, Thomas Edzear had a charter from (King) Robert Bruce of the lands of Kildonan, adjacent to which are those of kinhilt.
In confirmation of this we also find the name Edgar attaching to a hill on his property at Dromore."
Thank you to Mr. Agnew .
I can see myself that the name "Adair" probably came from how it was written down the way in which it was said (with an French/Irish/Scottish accent) in Latin, then translated back into English.
note: Duvenald of Limerick, natural son of MacMurchard,refer: