As a native Korean, I'm sure that both A and B will notice the confusion and switch to full names at around the fifth or sixth line. Korean full names tend to be short so it isn't cumbersome, in fact full names are often used in the first place exactly for that reason.
The real problem by the way starts with multiple persons with the same or almost identically sounding names. My own name (Kang Seonghoon) for example is shared with at least 100s of other Korean people, including one famous singer who got arrested later ;-)
Good point about use of full names. Since you are a native, you might not have noticed this, but I find that as a foreigner operating in professional settings, I only hear people referred to in English as $title+$family_name. Aside from my office mate, I can't think of the given name of anyone on campus.
Speaking of having identical names, the one that cracks me up is κΉμ μ.
The real problem by the way starts with multiple persons with the same or almost identically sounding names. My own name (Kang Seonghoon) for example is shared with at least 100s of other Korean people, including one famous singer who got arrested later ;-)