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?
Come to think of it, what bothers me isn't our name so much as the attitude of so many of my fellow citizens that the rest of the world is of no consequence. Our name puts a fine point on that narrow world view, regardless of whether it was intended that way.
So yeah, I'd rather see the culture change than the name.