I must thank my brother Iain who gathered all the following information. 

Caig

A Sept of the Clans FARQUHARSON and MacLEOD by Iain Caig. Copyright 1985

 

In SCOTLAND the surname CAIG derives from MacCAIG.
q.v. John CAIG and Andrew CAIG in the Parish of Buittle, 1684.

MacCAIG has many variant spellings;

 

v. MacCUAIG; Gaelic -- Cuthaig, (or cuckoo). A sept of the clan MacLEOD of Harris and Clan FARQUHARSON.

The tradition with regard to the origin of this sept is, that the father of a decaying family gave his child, in order to ensure long life to it, the name of the first thing which he met. This happened to be a cuckoo. Hence the name Mac-cubhaig, or MacCUAIG.

 

v. MacKaig ; Gaelic -- MacThaoig Irish -- MacTadhg, 'son of Tadhg.'

MacCaig, MacKaig is confined to Ayrshire and Galloway, but MacCaigs are also found in Arran, Carrick, Kintyre, Lisemore, Kerrara, Islay and elsewhere in Argyll and Dumfriesshire.

The name also appears as MacKEIG, MacKEGG and as CAIG in Galloway and Ulster.

Records show the following extracts.

A payment was made to a John Makhaig in Wigtonshire, in 1486.

Andrew MaAige, or MacCaig, a groom, was murdered in the blowing up of KIRK O'FIELD in 1567.

Donald M'Caoge an Irish variant of Caig appears in Irvine, 1681.

KNEEN (Manx Names), however says that MacCaog, in the Isle of Man, is form G. MacDhabhog, 'son of Dabhoc' a diminutive of David.

Janet Mackcaige was examined for the test in 1685.

Archibald McKeog was a rebel in the Kilcheran parish, Kintyre in the same year 1685.

Irish TADG appears in the Norse records as TAND or TAOKR, and in the Shetlands the name Tanderson is the equivalent to the Irish MacThaidhg.

The name appears in parish records spelt; M'AIG -1167 and in 1664 as MacCaig, MacKaig, MacKaige, McKaigh, MaKaig and McKigg.

In IRELAND CAIG is an anglicized form of the early Christian name TADHGH, TEIGE, meaning 'poet, philosopher.'

v.  TEAGUE, Thaldeus and Thady.

v.  MacTAGUE, MacTEAGUE, MacTIGUE and MacTEIGE.

MacThaidgh:  This name has many variant spellings.  It is not that of an actual sept, except in Co. Galway, where the MacTeiges are a branch of the O'Kelly's, but arose from the perpetuation of an ephemeral surname from the Christian name TADHG, TEIGUE.  It is chiefly found in Mayo and Donegal.

Also MacCaig and MacKeague.

v. MacKeague: A Northern Ireland name which is cognate with MacTeague and MacTeige.  Which has at least 14 different spellings.  Among these are MacCague (with and without the prefix Mac), as well as MacCaig, MacHaigh and MacKaig.