In the early 1800's when the Ojibway people fished the river and used it as a water supply at their encampments (including locations where the golf course now is), they traded with white settlers.
They did this at the mouth of the river which is now Port Credit (just south of the golf course). Furs, moccasins, woven baskets were typical of goods traded for knives, guns and trinkets.
When the Ojibways had nothing to trade they received the goods they desired with their promise of furs and other commodities to be received in the future. This kind of deferred payment plan was, of course, credit. Thus, Credit River.