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Your name originated in Renfrewshire, Scotland, where there is a place called Cochrane. The meaning is said to be "red brook" (Old Celtic). The name was carried to Ireland by Scottish planters, Ulster-Scots, or "Scotch-Irish" in American terminology. It's alleged that some Irish called Corcoran became Cochranes. I don't know if it's true but that sort of name swap did happen a lot in Ireland.