That works, since the USA is the only current country with America in its name. There was another, but it got split up. We don't call denizens of Mexico the UMS

That works, since the USA is the only current country with America in its name. There was another, but it got split up. We don't call denizens of Mexico the UMSians despite the country's name literally translating to the United Mexican States. Also, for a long time denizens in the US identified by state of birth or locality first before American. Civil War and World Wars changed that.