Must admit I seldom reply to an all capitals posting (modern equivalent of Green Ink ?) - the act of Union was 1702 by which time the Stanleys had been Lords of Man for just less than 300 years, a title which would soon pass to a grasping Scots family - the Murrays.
Mac is gaelic for son of - according to Moore
TEAR and TEARE, contracted from Mac-an-t-saoir, ' the carpenter's son.'

The importance attached by the Act 5, Ed. IV. (see introductory chapter)to the bearing of an English surname soon induced many of the less distinguished Irish families, of the English Pale, and its vicinity, to translate or disguise their Irish names, so as to make them appear English ; thus MAC-AN-T-SAOIEL was altered to CARPENTER.",

Compare (Gaelic) MACINTYRE, MACTIER, (Irish) MACENTIRE, MACATEER, MATEER, TEER, TIER.
On Island has a very long history in the records

MACTYR [1372],*M'TEARE, M'TERRE [1504], MACTERE [1511], TEARE [1599], TEAR [1611], TERE [1688].

It is much commoner in the north of the Island than the south.