Well I need to start learning some Korean, and improve my Chinese so I added the names of the countries to the title.
남한 - Namhan - being nam for south, not that different from Nan in Chinese and han being for the han people. Now this is a bit confusing, as the Chinese call themselves the han people as in hanyu. It turns out the Koreans still use some Chinese and call it hanja.
中国 - jung guo (first and second tones, I think) - is Chinese for middle country. A bit pompous really. But it is their view of the world. The guo is in simplified form. This has become so pervasive that even the Japanese use it. BTW, they call Chinese Hanji and their variant Kanji. So I just need to swap a few vowels and remember which country I am in.