Well, at least Canada has a proper name! We don't have a proper name.
Though implied that everybody knows what is being talking about when they refer to the country, think about this:
You call it America, technically you could be talking about an entire region spanning two continents.
You call it the United States, you could be talking about the United States of Mexico (the proper name of Mexico). And technically, Mexico is made up of United States of America since it is in North America.
And technically Canada could be known as the United Provinces of America...