The story
From Scotland, an anglicisation of the Scottish Gaelic Gaelic Mac Amhalghaidh ("son of Amhalghaidh"). From Ireland, an anglicisation of the Gaelic Mac Amhlaoibh ("son of Amhlaoibh") or Mac Amhlaidh ("son of Amhlaidh"). These Gaelic names are derived from the Old Norse personal name Áleifr and Óláfr.
Etymology from Wiktionary, CC BY-SA 4.0.