Scottish (Dumbartonshire) and Irish (Westmeath): Anglicized form of Gaelic Mac Amhalghaidh ‘son of Amhalghadh’, a personal name of uncertain origin.
Scottish (Hebrides) and Irish (Fermanagh): Anglicized form of Gaelic Mac Amhlaoibh or Mac Amhlaidh ‘son of Olaf’, from Gaelic forms of the Old Norse personal name Áleifr, Óláfr. Compare McAuliffe.
Dictionary of American Family Names, Oxford University Press, Mar 2003