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Scottish: topographic name for someone who lived near a steep or precipitous rock Older Scots crag craig. Compare the synonymous English Cragg . Manx: either a shortened form of Gaelic Mac Concharraige ‘son of Cu Charraige (‘hound of the rock’) or possibly of Mac Thorveig ‘son of Thorveig’ from the Old Norse personal name Thórveig (from the god's name Thórr + veig ‘pith strength’).
Source: Dictionary of American Family Names 2nd edition, 2022
This project includes variants, such as: Craigh, Craigie, Cragg, Craggs, Carrick, Craige, Creag, Craik, Cregg