Although using some convention to separate the given name from the surname (either with the hyphen between the two syllables of the given name, Min-ho or by joining them as one, Minho) makes it easier for the viewers and it’s the way most people actually write their names, it was decided on Viki many years ago among the volunteers that the names would be written without hyphens, because apparently subbers thought adding this hyphen was too much of an extra job (LOL!). Therefore you don’t see hyphens in subtitles nowadays.
In case of discrepancy, everyone follows the guidelines of the Chief Editor.
For a long time now, I have been waging a campaign for using RR (Revised Fomanization), for all Korean words in our subtitles, including names. You know, the official spelling of Hangul which is a state law in Korea since 2000. Because the old spelling was just something that made sense to English speakers, and not so much for the rest of the world. Like “oo” instead of “u” and “u” instead of “eo” (a very open ò). Why should we write hyung instead of the correct hyeong and noona instead of nuna?
Same for names. Yes, private individuals still have a choice on how to romanize their names in Korea, they weren’t obliged to change them, although it’s warmly encouraged.
Usually we make an exception for five very common names, which we keep in their usual anglicised form:
Kim (김, normally Gim) As of the South Korean census of 2015, there were 10,689,959 people by this name in South Korea or 21.5% of the population.
Lee (이, normally I or Yi - but Joseon kings are written Yi). the second-most-common surname in Korea. As of the South Korean census of 2015, there were 7,306,828 people by this name in South Korea or 14.7% of the population. Though the official Revised Romanization spelling of this surname is I, South Korea’s National Institute of the Korean Language noted in 2001 that one-letter surnames were quite rare in English and other foreign languages and could cause difficulties when traveling abroad. However, the NIKL still hoped to promote systemic transcriptions for use in passports, and thus recommended that people who bore this surname should spell it Yi in the Roman alphabet. However, the majority of South Koreans with this surname continue to spell it as Lee, because conditions for changing passport name is strict.
Park (normally Bak)
Kang (강, normally Gang) Sixth more popular Korean surname.
Choi ( 최, normally Choe)
Again, follow what your moderator/editor wishes.