There are various names of Korea in use today, derived from ancient kingdoms and dynasties. The English name Korea is an exonym derived from the Goryeo period and is used by both North Korea and South Korea in international contexts. In the Korean language, the two Koreas use different terms to refer to the nominally unified nation: Chosŏn (조선) in North Korea and Hanguk (한국) in South Korea.
See also: History of Korea
The earliest records of Korean history are written in Chinese characters, despite the languages being unrelated. Even after the invention of hangul, Koreans generally recorded native Korean names with hanja, by translation of meaning, transliteration of sound, or even combinations of the two. Furthermore, the pronunciations of the same character are somewhat different in Chinese and Korean, and have changed over time.
For all these reasons, in addition to the sparse and sometimes contradictory written records, it is often difficult to determine the original meanings or pronunciations of ancient names.
Until about 2000 years ago, northern Korea and southern Manchuria were controlled by Gojoseon. In Chinese records, it was written as 朝鮮, which is pronounced in modern Korean as Joseon (조선). Go (古), meaning "ancient," distinguishes it from the later Joseon Dynasty.
The Chinese characters phonetically transcribed a native Korean name, thought to have been then pronounced something like "Jyusin" (pronounced JyuShin) Since "Jyusin" sounds and means "given," This may refer to the korean Trinity of Deities religion dominating philosophic thought at the time, where the common belief is that their land is "given", bestowed or gifted to them by the 3 heavenly Gods.  Some speculate that it also corresponds to Chinese references to 肅愼 (숙신, suksin), 稷愼 (직신, jiksin) and 息愼 (식신, siksin), although these latter names probably describe the ancestors of the Jurchen.
Other scholars believe 朝鮮 was a translation of the native Korean Asadal (아사달), the capital of Gojoseon: asa being a hypothetical Altaic root word for "morning," and dal meaning "mountain," a common ending for Goguryeo place names.
The character 朝 means both "dynasty" (read as cháo in Chinese) and "morning" (read as zhāo in Chinese), while 鮮 may translate to "fresh" or "savory," often used to describe rarity. It is notable that the characters for Joseon, i.e. 朝鮮, are read as Cháoxiǎn in Mandarin Chinese. The first character is read as cháo, which is identical to the way that this character is pronounced when it is used to write the Chinese word for "dynasty" rather than the way that it is pronounced when used to transcribe a rare word for "morning," and the second character is read as xiǎn with a falling-rising contour tone, which is a special reading of this character that is used only when pronouncing the name of Cháoxiǎn (Joseon). The Chinese evidence suggests that 朝鮮 was never intended to transcribe the meaning of any word, but rather to transcribe the pronunciation of a Korean or Manchurian ethnonym.
Around the time of Gojoseon's fall, various chiefdoms in southern Korea grouped into confederacies, collectively called the Samhan (삼한, "Three Han"). Han is a native Korean root for "leader" or "great," as in maripgan ("king," archaic) and harabeoji (originally hanabi, "grandfather"). It may be related to the Mongol/Turkic title Khan.
Han was transliterated in Chinese records as 韓 (한, han), 幹 (간, gan), 刊 (간, gan), 干 (간, gan), or 漢 (한, han), but is unrelated to the Chinese people and states also called Han. (See: Transliteration into Chinese characters).
Around the beginning of the Common Era, remnants of the fallen Gojoseon were re-united and expanded by the kingdom of Goguryeo. It, too, was a native Korean word, probably pronounced something like "Guri", transcribed with various Chinese characters: 高句麗/高勾麗/高駒麗 (고구려, Goguryeo), 高麗 (고려, Goryeo), 高離 (고리, Gori), or 句麗 (구려, Guryeo). In 高駒麗, the character 高 ("high") is an adjective, rather than a part of the transliteration. The character 麗 is sometimes pronounced ri.
The source native name is thought to be either Guru (구루, walled city) or Gauri (가우리, "center"; c.f. Middle Korean gavɔndɔy and Standard Modern Korean gaunde 가운데).
The theory that Goguryeo referenced the founder's surname has been largely discredited (the royal surname changed from Hae to Go long after the state's founding).
In the south, the Samhan resolved into the kingdoms of Baekje and Silla, constituting, with Goguryeo, the Three Kingdoms of Korea. In 668, Silla unified the three kingdoms, and reigned as Unified Silla until 935.
The succeeding dynasty called itself Goryeo (고려, 高麗), in reference to Goguryeo. Through the Silk Road trade routes, Muslim merchants brought knowledge about Silla and Goryeo to India and the Middle East. Goryeo was transliterated into Italian as "Cauli," the name Marco Polo used when mentioning the country in his Travels, derived from the Mandarin Chinese form Gāolí. From "Cauli" came the English names "Corea" and the now standard "Korea" (see Western usage below).
In 1392, a new dynasty established by a military coup revived the name Joseon (조선, 朝鮮). The Chinese characters were often translated into English as "morning calm," and Korea's English nickname became "The Land of the Morning Calm"; however, this interpretation is not often used in the Korean language, and is more familiar to Koreans as a back-translation from English.
When Korea came under Japanese rule in 1910, the name reverted to Joseon (officially, the Japanese pronunciation Chōsen). During this period, many different groups outside of Korea fought for independence, the most notable being the Daehan Minguk Imsi Jeongbu (대한민국 임시정부, 大韓民國臨時政府), literally the "Provisional government of the Great Han people's nation", known in English as the Provisional Government of the Republic of Korea (民國 = 民 ‘people’ + 國 state/nation’ = ‘republic’ in East Asian languages).
In 1948, the South adopted the provisional government's name of Daehan Minguk (대한민국, 大韓民國; see above), known in English as the Republic of Korea. Meanwhile, the North became the Chosŏn Minjujuŭi Inmin Konghwaguk (조선 민주주의 인민공화국, 朝鮮民主主義人民共和國) literally the "Joseon Democratic People's Republic", known in English as the Democratic People's Republic of Korea.
Today, South Koreans use Hanguk to refer to just South Korea or Korea as a whole, Namhan (남한, 南韓; "South Han") for South Korea, and Bukhan (북한, 北韓; "North Han") for North Korea. South Korea less formally refers to North Korea as Ibuk (이북, 以北; "The North").
North Koreans use Chosŏn, Namjosŏn (남조선, 南朝鮮; "South Chosŏn"), and Bukchosŏn (북조선, 北朝鮮; "North Chosŏn") respectively.
The Korean language is called Hangugeo (한국어, 韓國語) or Hangukmal (한국말) in the South and Chosŏnmal (조선말) or Chosŏnŏ (조선어, 朝鮮語) in the North. The Korean script is called Hangul (한글) in South Korea and Chosŏn'gŭl (조선글) in North Korea. The Korean Peninsula is called Hanbando (한반도, 韓半島) in the South and Chosŏn Pando (조선반도, 朝鮮半島) in the North.
In Chinese-speaking areas such as mainland China, Hong Kong, Macau, Singapore, and Taiwan, the Korean Peninsula is usually called Cháoxiǎn Bàndǎo (Simplified Chinese: 朝鲜半岛; Traditional Chinese: 朝鮮半島), but it is also less often called Hán Bàndǎo in Hanyu Pinyin (Simplified Chinese: 韩半岛; Traditional Chinese: 韓半島).
Until recently, the People's Republic of China tended to use the historic Korean name Cháoxiǎn (朝鲜 "Joseon"), by referring to South Korea as Nán Cháoxiǎn (南朝鲜 "South Joseon"). Since establishing diplomatic relationship with South Korea 1992, China has used the names that each of the two sides prefer, by referring to North Korea as Cháoxiǎn and to South Korea as Hánguó (韩国 "Hanguk"). The Korean language can be referred to as either Cháoxiǎnyǔ (朝鲜语) or Hánguóyǔ (韩国语), although many people argue that the former is more correct, as China itself has a sizeable minority of ethnic Koreans (朝鲜族 Cháoxiǎnzú) who use the historic name.
Taiwan, on the other hand, uses the South Korean names, referring to North Korean as Běihán (北韓 "North Han") and South Korean as Nánhán (南韓 "South Han"). As the Republic of China recognized South Korea but not North Korea, Hánguó (韓國) had been used to refer to the whole Korea and Taiwanese textbooks treated Korea as well as China as united nations. The Ministry of Foreign Affairs of the Republic of China under the Democratic Progressive Party Government now considers North and South Koreas two separate countries. However, the people in Taiwan still refer to North Korean as Běihán (北韓 "North Han[guk]") and South Korean as Nánhán (南韓 "South Han[guk]") while use of Cháoxiǎn (朝鮮) is generally limited to ancient Korea and the Republic of China never maintains diplomatic relations with the Democratic People's Republic of Korea. The Korean language is usually referred to as Hánguóyǔ (韓國語) or Hányǔ (韓語).
Similarly, people in Hong Kong and Macau call North Korea Bak Hon (北韓 "North Han") and South Korea as Nam Hon (南韓 "South Han").
In Chinese language used in Singapore, North Korea is usually called Cháoxiǎn (朝鲜 "Chosŏn") with Běi Cháoxiǎn (北朝鲜 "North Chosŏn") and Běihán (北韩 "North Han") less often used, while South Korea is usually called Hánguó (韩国 "Hanguk") with Nánhán (南韩 "South Han[guk]") and Nán Cháoxiǎn (南朝鲜 "South Chosŏn") less often used.
In Japan, the names preferred by each of the two sides is used, so that North Korea is called Kita-Chōsen (北朝鮮; "North Chosŏn") and South Korea Kankoku (韓国 "Hanguk"). In January 2003, several newspapers switched from spelling out North Korea's much longer official name (朝鮮民主主義人民共和国) at least the first time the country is mentioned to always using its short form instead. The Korean language is most frequently referred to in Japan as Kankokugo (韓国語) or Chōsengo (朝鮮語). It is also referred to as "Chōsen-Kankokugo" (朝鮮韓国語) or "Kankoku-Chōsengo" (韓国朝鮮語). However, when NHK broadcasts a language instruction program for Korean, the language is referred to as Hangurugo (ハングル語) meaning language of the Hangul writing system. Some people refer to it as Koriago (コリア語; Koria is the transcription of Korea) meaning the language of Korea. These term is not used in ordinary Japanese, but was selected as a compromise to placate both nations in a euphemistic process called kotobagari. There is a trend to use the transcription of English Korea (コリア, Koria) and Korean (コリアン, Korian) in print media in order to avoid making an implied political statement.
In Vietnam, people call North Korea Triều Tiên ("Chosŏn") and South Korea Hàn Quốc ("Hanguk"). Prior to unification, North Vietnam used Bắc Triều Tiên (Bukchosŏn) and Nam Triều Tiên (Namjosŏn) while South Vietnam used Bắc Hàn (Bukhan) and Nam Hàn (Namhan) for North and South Korea, respectively. After unification, the northern Vietnamese terminology persisted until the 1990s. When South Korea reestablished diplomatic relations with Vietnam in 1993, it requested that Vietnam use the name that it uses for itself, and Hàn Quốc gradually replaced Nam Triều Tiên in usage.
Both South and North Korea use the name "Korea" (or equivalent) when referring to their countries in English or other western languages.
Because of the coexistence of "Corea" and "Korea" in the 19th century English publications,  some Koreans believe Japan, around the time of the Japanese occupation, intentionally standardized the spelling on "Korea," so that "Japan" would appear first alphabetically. Both major English-speaking governments of the time (i.e. the United States and the United Kingdom and its Empire) used both "Korea" and "Corea" until the early part of the Japanese occupation.    "English books and maps published through the 19th century generally spelled the country's name as Corea, as did the British government in laying the cornerstone of its embassy in Seoul in 1890 with the name "Corea." But sometime in the early 20th century, "Korea" began to be seen more frequently than "Corea" - a change that coincided with Japan's consolidation of its grip over the peninsula." Most evidence is circumstantial, including a 1912 memoir by a Japanese colonial official that complained of the Koreans' tendency "to maintain they are an independent country by insisting on using a C to write their country's name." 
Where large immigrant populations were established outside of Korea before its division, the communities tend to maintain the identity of the former Korean nation, without associating with either the North or South Korean governments.
Subjects of former Goryeo who moved to Russian and Central Asia call themselves Goryeoin (고려인; 高麗人; literally "person or people of Goryeo"), or корейцы in Russian. Many Goryeoin are living in the CIS, including an estimated 106,852 in Russia, 22,000 in Uzbekistan, 20,000 in Kyrgyzstan, 17,460 in Kazakhstan, 8,669 in the Ukraine, 2,000 in Belarus, 350 in Moldova, 250 in Georgia, 100 in Azerbaijan, and 30 in Armenia.
In Japan, those who moved to Japan before and after the annexation of the Korean Peninsula usually maintain their distinctive cultural heritages (such as the Baekje-towns or Goguryeo-villages). Those who live in Japan with Korean nationality are now called Zainichi /Kankokujin, (/韓国人) by the Japanese, a term that is also used for people of Korean ancestry living in Japan who do not profess a preference for either North or South Korea.
"Subjects of former Goryeo who moved to Russian and Central Asia call themselves Goryeoin (고려인; 高麗人; literally "person or people of Goryeo"), or корейцы in Russian." - this is a common mistake found in some English websites!
Koreans who live in Russia and former USSR are not "Subjects of former Goryeo”, they started to migrate to the territory of former Russian Empire only since the second part of 19th century. But Goryo was overtaken by Joseon dynasty in 1392!
The Russian words кореец/koreets - singular or корейцы/koreytsi – plural, are not the forms of Korean word Goryeoin but originates from the western name of Korea (Корея/Koreya in Russian) so in Russian, кореец/koreets means a person from Korea or of Korean origin but not a person from medieval Goryo!
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