When the US Army was building the route, it was the Alcan Military Project, or something similarly worded. So it was usually called the Alcan or the Oil-Can (for all the empty oil drums left along the route).
On April 1, 1946, six months after the end of the war, the US Army officially handed over the route and associated facilities to the Canadian Army. The Royal Canadian Engineers became responsible for the maintenance and construction of the Alaska Highway. Then along came springtime and the Canadians realized there was a lot of work ahead of them to make the route a driveable highway. My Dad was one of the fellows who did some of the maintenance work in the 1950s. And so I have a copy of the book that documents the Canadian Army's maintenance and construction activities from 1946 to 1964.
So, anyway, I can understand Americans still using the term Alcan 70 years later in reference to the military project. But gee, the US purchased Alaska from Russia just 149 years ago and it became a state only 57 years ago, so I guess you wouldn't mind if we call it Russia. :B