This is a very late reply, but I hope if this can help you a little. Seeing this and your other question thread, I suppose you read Clamp's "신 춘향전(新春香傳)," a manga by Japanese artists. It was very interesting that they created a colorful story with a completely new viewpoint based on a classic Korean tale.
Anyway, here are the answers:
암행어사: Amhaengeosa (if you feel this is too long, write as Amhaeng-eosa instead)
Note that 蓮姫's pronunciation and writing are changed from 련희 (Ryeonheui) to 연희 (Yeonheui) in South Korean, since no R/L sound may be placed at the beginning of a word. This rule does not extend to borrowed words other than ancient Chinese origin though, so it is 라디오 (Radio), not 나디오 (Nadio) or 아디오 (Adio). Also, North Koreans discarded this rule, so everybody with the family name Lee is written and pronounced as 리XX (Ri-XX, or XX Lee) rather than 이XX (I-XX, or XX Yi, but they are usually romanized as "XX Lee" in South Korea too).