Adams, Adamson
Adams, Adamson—MAC ADAIM.—Some families of this name are a branch off from the McGregors of South-Western Scotland, who later assumed the name of Grier, etc. Scottish families of the name of Adamson settled in Cumberland, and the name in some of its anglicised forms is found in various parts of Ulster. Adam as a Christian name is pretty common in the North of Scotland, probably arising from the Irish missionary, St. Adamnan. The Mac Conshnámha sept in North Connacht have assumed the name of Adams.
Alphabetical Index of Anglicised Surnames in Ireland
See also Woulfe’s Irish Names and Surnames
… and O'Hart's Irish Pedigrees