Almost all Korean names have corresponding Chinese names. Although Korean has one-to-many Chinese characters, when they choose names, they will choose Chinese names themselves, which is fixed. For example, ZHANG SAN's English name on his passport is Zhang San. Just looking at English, you don't know whether his Chinese name is Zhang San or Zhang San. You have to go and see what his name is on his ID card.
Therefore, when translating Korean names, go back and find out what the Chinese name the person has already chosen. Generally, it is not transliterated unless the Chinese name of the person cannot be found. For example, park geun-hye is not transliterated, but her Chinese name is actually called this name. The transliteration can be Park Jin-hui, Park Jin-hui and so on.
However, in recent years, there have been some cases in which Korean proper words are used for naming, and some people even use foreign words for naming. The Korean names of proper words are transliterated, such as Anglenala and Jin Hena, while those who use foreign words tend to transliterate with the foreign words themselves.
The same is true in literary and artistic works. Some people have been assigned to follow the established rules, but no one has been transliterated. Transliteration follows the public, and whoever turns it early and makes it highly accepted by the public will be called by what name. Translation into Korean dramas is usually transliterated by the subtitle group itself, but some characters will have their Chinese names in the drama, and the subtitle group will change the translation accordingly.