Bain, Bayne
Bain, Bayne—This name in Tulloch, Scotland, appears also as Baine. According to Dr. McBain, one of Scotland's best historians and antiquarians, a John Makferquhar Mac Gillebane lived near them in 1555, which evidently shows that the names are anglicisations of McGilvane (Mac Giollabhain). The other anglicised forms are McIlwaine, McGilbane, and White. See White.
Alphabetical Index of Anglicised Surnames in Ireland
See also Woulfe’s Irish Names and Surnames
… and O'Hart's Irish Pedigrees