Where I grew up, a brook (a watercourse smaller than a creek which is smaller than a river) was called a run. In New England, it would be a brook, but if you went far enough north, it might become a stream. Down here in Virginia, they call it a branch.
I had not realized it could also be a bayou, arroyo, a slough, or a cañada.
Hat tip to Walter Olson.