You might know of well-known Soviet musician Viktor Tsoi, whose name in Hangul is 최 and in Cyrillic is Цой.
The thing is that now his name seems to be written as 초이. My guess is that it has something to do with 최 being pronounced as [t͡ɕʰwe̞] ~ [t͡ɕʰø̞] (according to the Wiktionary entry for that syllable). What changed? Is 최 ever pronounced as [t͡soj], for example in Kimch'aek where his ancestry may be traced back to?