I think it would be helpful to have an additional hint besides just the country name. Many of these are impossible to guess with some kind of context. Add the population or the continent or something to help us have a puncher's chance.
I think the pronunciation should be considered when picking the meaning of the character for North Korea. Morning would be zhāo instead of cháo (so it would mean facing/any other term represented by that pronunciation), while xiǎn would mean rare/less as in 鲜为人知
"'鲜'又假借为'尟',读作xiǎn,表示少之义。" - According to Baidu Baike
Thanks for the comment! After doing some digging, what makes the most sense to me is to go by the interpretation on the pages of the Chinese embassy in North Korea - "朝日鲜明之国"
Typing North Korea "correctly" answers the entry for South Korea, though!
Yeah, the Koreas are a bit of a headache, which is why this quiz is pretty lenient. See: https://en.wikipedia.org/wiki/Names_of_Korea
"'鲜'又假借为'尟',读作xiǎn,表示少之义。" - According to Baidu Baike