I was wondering if having only one character in your name is common or not. I was born in the US and not very familiar with the culture, so I'm not sure if it's odd or out of place. I've seen other people names that have 2 characters like Min-jun and such but I feel out of place whenever I say my name with those who are familiar with the culture.
현 is a perfectly normal name. I even know someone with that name.
Single-character given names are not that uncommon, and you could find many well-known people with single-character names: 김구 (independence fighter), 신립 (a general in Joseon era), 최영 (another general in Goryeo era), 심훈 (a novelist in the Japanese colony era), 김훈 (a famous contemporary novelist), 최훈 (a comic artist), 진영 (a congressman), 허재 (a basketball player), 강민 (a professional Starcraft player), and on and on.
You might feel "out of place" because in Korean-American society some people have a habit of using only the first character of their given name. E.g., someone might be named 김현석, and then he might write his name as Hyun Seok Kim, and go by just "Hyun" most of the time. So when a Korean-American hears your name is Hyun, they might not be sure if it's your "real" Korean name or if you have another character after it which you just chopped off.
However, if you were in Korea, such a practice won't happen and nobody would find anything strange with 현. :)
Nah man not at all. And personally I find single-character names (외자 이름) pretty cool, so no worries. There have been some famous people with that kind of name, so, while it's definitely not common, it's not weird at all. If it makes you feel any better, there are people with two-character last names, so their full name either end up in 4 characters, or 3 characters with a single character first name.