Wordorigins.org

Quebec is an Algonquin word meaning river narrows, a reference to the St. Lawrence river as it passes the site of Quebec City. The name, spelled Quebecq, first appears on a 1601 map. The name originally referred to the city, which was founded in 1608. It was applied to the territory formerly known as New France after its acquisition by the British. The name was changed to Lower Canada in 1791 and then back to Quebec in 1867 with the formation of the Canadian Confederation.

(Sources: Dictionary of Canadian Place Names; Illustrated Dictionary of Place Names)