Here is a flag of what could have been America if the Nazis have won WW II. If you are asking what Nazi America would be called as an alternate name, then I would say the "Nationalist-Socialist States of Amerika".
Government: Fascist Puppet State of Nazi Germany
Head of State: Fuhrer Adolf Hitler
Capital: New York City
Population: 312,828,000 (mostly Germans and English)
Established: June 15th, 1947
Ideology: Anti-Semitism, Anti-Liberalism, Fascism, Nationalist-Socialism, Anti-Capitalism, Anti-Communism, Anti-Homosexuality, Anti-Abortion, Nordic-Nationalism, Nazism, Anti-Anarchism