Livingstone
Livingstone—This name is the anglicised form of two Scottish sept names, one in the North, known as Mac Leay, in Gaelic Mac Dhuinnsheibhe, some of whom assumed the name of Dunlap also, the other, a Dumbarton Co. sept, who were physicians; in Gaelic Mac An-Leigh, the "Son of the Doctor." William Livingstone, the bard, belonged to the Argyle sept of Mac Dhuinnshleibhe. This latter name is anglicised to M'Clew and M'Glew in Ulster.
Alphabetical Index of Anglicised Surnames in Ireland
See also Woulfe’s Irish Names and Surnames
… and O'Hart's Irish Pedigrees