The official local name for South Korea is Dae Han Min Guk and its abbreviated form is Hanguk. Han [
] refers to Korea in South Korea, but there is another Han [
]. Han also means China's dynasty (206 BC-8 AD, 25-220 AD) and Han-Chinese. In short, both Korea and China are called Han in South Korea. Two Hans are denoted as different character in Chinese characters but cannot be distinguished in Hangul. As a matter of convenience, this article calls the former Han2 and the latter Han4 according to China's Pinyin Romanization.
This homonym makes many Koreans falsely recognize that Chinese culture or words have Korean origins. For example, Traditional Chinese Medicine is called Hanbang in Korean. Hanbang is a Sino-Korean word, originated in a Sino-Japanese word Kanpo, which means Chinese method and was made to distinguish the tranditional medicine from Western medicine, newly imported from Dutch in the Edo period (1603-1868). Han4bang has changed into Han2bang in South Korea, with seldom Koreans noticing, and then Han2bang become Korea's own original method. A increasing number of Koreans ignorant about Chinese characters accelerate this tendency.
By the way, Han4seong is an old name for Seoul and the Chinese still use "Han4 Cheng2," the Mandarin Chinese pronunciation of Hanseong, because Seoul is a native word standing for capital and does not have corresponding Chinese characters. But Han4 Cheng2 may imply a Chinese city. The South Korean government once asked China to notate Seoul as 
[shou3 wu1 er3], but was rejected. Korea is always submissive to China.