Korea
wiktionary
First attested as Core in the 1598 English translation of the 1596 Itinerario of Jan Huyghen van Linschoten, from the original Dutch Core, itself from Portuguese according to van Linschoten's account.
Ultimately a sixteenth-century borrowing by Europeans from some variety of Chinese—perhaps specifically Mandarin 高麗/ 高丽 (Gāolí)—after Sino-Korean 고려(高麗)(Goryeo), which was Korea's official name between 918 and 1394 and continued to be commonly used by Chinese people to refer to the country for centuries thereafter. This was itself a shortening of 高句麗/ 高句丽 (“Goguryeo”), an ancient Korean kingdom in the first millennium. Doublet of Goryeo, directly from Korean.
The earliest form in Europe was probably William of Rubruck's Medieval Latin Caule (clearly from Early Mandarin), but this is not ancestral to the modern European names. Some Korean authors claim an Arabic intermediary instead, but the actual medieval Arabic word for Korea was a variant of السيلى (al-sīlā, see also Silla).
The spelling Corea was more common in Early Modern English.
etymonline
Korea
by 1690s, from Chinese Gao li, name of a dynasty founded 918, literally "high serenity." Japanese Chosen is from Korean Choson, literally "land of morning calm," from cho "morning" + son "calm." Related: Korean (1610s). In early use Corea, Corean.