Was the US of America ever called the US of north America?
No the United States of America was never known as the United States of North America.
The American continents are located in both northern (North and Central America) and southern (South America) hemispheres. The United States of America (sometimes improperly called simply "America" is on the North American continent and therefore in the northern hemisphere. The US Civil War is sometimes called a war between "north" and "south" but in that case both sides were in the USA, in North America, and in the northern hemisphere.