The Irish surname McInally is an anglicized form of the Gaelic name  Mac an Fhailghigh meaning “son of the poor man.” When found in Ulster it is  an anglicized form of the Gaelic name Mac Con Uladh meaning “son of the hound of Ulster.” Most present day name-bearers are found in East Ulster and specifically the counties of Armagh and Monaghan, with a small number of families found in counties Mayo and Galway in the western province of Connaught.