EFL Geek posted relatively recently (a few months back) about English Nicknames in Korea.
Me, I despise them. I basically ignore any English name offered to me by someone who wasn’t born with it. I have managed to create French- and Korean-language identities for myself just fine without a new, fake name that isn’t really mine.
I also think that the self-imposition of an English name is silly, since it reinforces the notion that Koreanness is incompatible with English-speaking, a ridiculous notion. I understand some people do it for fun, and sometimes in class I make an effort to acknowledge it if a student insists on being called “Shark” or “Winston” or the like, but usually I explain that I prefer to call people by their real names.
Finally, I laugh whenever anyone says Korean names are hard to pronounce. It’s three syllables, almost always very close to phonetically written. It’s far from hard. Russian names, those could be hard. Korean names are NOT hard to pronounce; it’s just that they’re hard to memorize in large groups.
And yeah, there are exceptions: Bum Suck is a name I never encountered till I arrived in Jeonju, and I’ve met three since. I also had a female student named Mi Seok (Me Suck), who had alright English but probably hadn’t figured out why I looked shocked the first time I heard her name. In those cases, I’d only consider explaining the way it sounds to an Anglophone if the person was planning to go abroad.