The first problem is that you never know what form of someone's name you're going to get. If I ask a Korean what their name is, sometimes they give me their English name, sometimes they give me their name in standard Korean family name/given name order, and sometimes they give me their Korean name in Western given name/family name order. It's most annoying when they give an English name that they don't actually use, because then you won't know when someone is calling them with their Korean name. If they give you both English and Korean names, you now have twice as many names to remember. And a lot of Korean names said backwards (i.e., given name/surname) are actually valid Korean names forwards, so you need to clarify with them which part is their given name, since it's inconsistent when Koreans speak with foreigners.
For the sake of people trying to learn Korean names, let's just make it easier. If a foreigner asks you your name, tell them your Korean name in standard family name/given name order, and optionally follow it up with, "But please call me
Of course, it's near impossible to learn people's names by listening to conversations, since everyone calls each other "older sister", "older brother", "teacher", etc.
Anyway, in a totally unrelated topic, for some reason the Korean word for "sweetheart" is the same as the word for "self". I found this quite confusing at first - I'd hear people at coffee shops talking about 자기 (chagi) this and 자기 that, and I wasn't sure if they were talking about other people or themselves, since one of the first homework assignments we had in class was a 자기 소개, or a self-introduction (or were we supposed to introduce our significant others? hmm). It turns out that when used to mean "self", it's almost always used in a third-person sense, such as, "She thinks so highly of herself. She has some serious 공주병 going on." But you can complicate it further by talking about your sweetheart and what they think of themselves, which would use the same word 자기 for two totally different meanings. Context is super important in Korean.
아이고. Need to study more.