Cook is English occupational: Middle English cok/cook from Old English cōc, naming a cook, a seller of cooked meats, or someone keeping an eating house. Large households and inns needed that role, so the surname arose in many places at once.
Irish and Scottish Cook is often the same English word; some Gaelic Mac Cúg lines were anglicized to Cook. German Koch and other European "cook" names may be translated to Cook in America. The core gloss stays kitchen work, not a place-name.