Not just last names. A lot of Korean first names are more or less the same or very similar. When I was at university, I had two other girls in the class of 30 with the same last name (Kim) and first names (Korean equivalent of Mary). To differentiate three of us in the same class, the faculty labeled me Mary Kim A, the second girl Mary Kim B and the third one Mary Kim C. This tops any residential school in Northern Ontario.
Funny we had Kim A. & Kim B in my 1st and 2nd grade class - I was Kim B. My last name actually begins with a B and the other Kim's last name actually began with an A. so it worked out well for us - even our middle names were the same!