Derived from the region in Scotland called Moray seaboard settlement. A notable bearer of this surname was General James Murray (1721-1794), who was the first British Governor-General of Canada.
The town of Garryowen was named after the old Irish tune Garry Owen which was one of Lt. Col. George Armstrong Custer's favorite marching songs. Garry Owen is an old Irish quick-step that can be traced back to the 1800s. it is known to have been used by Irish regiments as a drinking song.
The claim that it is of Micmac origin is probably coincidental. The Micmac word Quoddy or Cady was rendered by the French as cadie and meant a piece of land or territory. Source: Hamilton, William B. (1978): The Macmillan book of Canadian place names, Macmillan of Canada, Toronto, p. 129.