As far as I can tell the name is just 막골리(makkoli). Makkoli is a traditional Korean rice wine of sorts. It sort of has a white milky, chalky flavor that most people tend to love or hate. This restaurant specializes in all sorts of traditional Korean drinks, including 4 kinds of makkoli. Though the restaruant specializes in traditional korean drinks, the ambiance is more of a fusion of many different cultures. It is completly decked out in bamboo, and it has a bar that reminds me of a japanese style establishment. Not only that, but they had hookas available to smoke, if that's your style.
As I said, it's sort of in a random part of town. It's located about 5 minutes walk from Sookmyung women's university station. Go out exit 1 (?) and turn around and go around the corner. From there, go down the first street on your right, it will be on your left, across the street from a Chinese Food restaurant (which is also decent). Didn't see an English menu, but the staff looked young, so they probably speak a little English.