Many countries include 'Democratic' or 'People's' in their names, even though they are not democratic and do not serve their people. Examples:
Democratic People's Republic of Korea
Lao People's Democratic Republic
People's Democratic Republic of Algeria
Democratic Republic of the Congo
And German Democratic Republic (East Side) in 1949–1990.
None of these states are democratic, power and wealth are concentrated in the hands of a small ruling elite. Who are they fooling with these names?
No. It is not incorrect. It is simply that "America" can refer to the USA, or it can refer to a continent if you consider NA/SA to be a single continent. Similarly, "Georgia" is a US state but also a country.