Ó Conaire
Ó CONAIRE—I—O Connery, O Conrey, Connery, Conry, (Conroy), &c.; 'descendant of Conaire' (probably dog-keeper, an ancient Irish personal name); an old Munster surname, common throughout the province; to be distinguished from Ó Conraoi, which see.
Alphabetical Index to Irish Surnames