United States of America -> America

United States of Mexico -> Mexico

Republic of France -> France

Kingdom of Norway -> Norway

People's Republic of China -> China

Commonwealth of Australia -> Australia

Federated States of Micronesia -> Micronesia

Republic of South Africa -> South Africa

Republic of Korea -> Korea

Do you begin to see the trend here?

Note that the Federated States of Micronesia does not include all of Micronesia -- there are several other countries in that geographic region. Nor does the Republic of South Africa include all of South Africa. Nor does the Republic of Korea include all of Korea.

Besides, the USA was the first, and so far only, one to use "America" in its name, so it gets grandfather rights.