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We call them by what they want us to call them as. South Korea is known formally as Republic of Korea, North Korea is known as Democratic People's Republic of Korea. Mean While South Koreans referr to their country as Dae Han Min Guk, While North Korea calls themselves Chosun Minju Juui Inmin Gonghwaguk.
Sometimes we call them such for convenience, other times its because its what we've been calling them for a long time. In most cases, they have official English names, some of which are the same as what it is in their language, other times its some thing other.