In dicussions of Korea, it is good to note that "South Korea" is the common term for the Republic of Korea. English millitary personnel will often use the term "the ROK" in reference to the country. North Korea's long form name is the Democratic People's Repulic of Korea, or, PRK.
References to the wording is available from the CIA World Factbook:
CIA World Factbook: South Korea
http://www.cia.gov/cia/publications/factbook/geos/ks.html
- conventional long form: Republic of Korea
- conventional short form: South Korea
CIA World Factbook: North Korea
http://www.cia.gov/cia/publications/factbook/geos/kn.html
- conventional long form: Democratic People's Republic of Korea
- conventional short form: North Korea