@villainousfriend This is the most official source for Korean romanization: https://www.korean.go.kr/front_eng/roman/roman_01.do There are a good amount of small tweaks you can make in non-official entertainment uses--for instance, the official romanization of 희 (often used in person names) is "hui" but can safely be replaced by "hee" because it's easier to read and there is basically no danger of confusion. I personally dislike "eo" for ㅓ, though I use it for technical work of course, and use "u" (as it "gut") whenever I can for creative/entertainment uses.

Also, most modern Koreans have their own preferred alphabetic orthography for their names so the official romanization can be considered basically moot in favor of their preference. In practice this means you can use whatever spelling you like for fictional characters. In personal names the official Korean romanization is basically for historical personages who didn't have preferred Western spellings, or others who don't have a personal preference or whose preference can't be known.