Khmer names:
w. capital at Phnom Penh and democratic - Democratic Kampuchea
If America is both Capitalist and Totalitarian: America Inc.
One thing I noticed was missing was a selection of theocratic state names; I was hoping my Protestant Viking State had a name. Perhaps as a starting point: Catholic: the Diocese of Scandinavia (France/England/etc)... I don't know what the Protty equiv of a diocese is though.
More ideas.
If Carthage is in the Middle East and Christian: Kingdom of Jerusalem
If Ethiopia is Muslim: Sultanate of Adal
If Jewish: Kingdom of Semien
If Britain is Fascist: New British Empire (or Second British Empire, or perhaps just British Empire)
If Britain is a Nazi German vassal: British Union
If Britain is Theocratic and not Muslim: Holy Britannian Empire
If Britain is Theocratic and Muslim: Caliphate of England
If America is Theocratic and Christain: Lord's Believers