I, for one, care. I'm not exactly what you'd call "patriotic", but for some reason, I always get into international competition. I'm not a Soccer fan, but I enjoy the World Cup. I enjoy certain Olympic events. I'm sure that I'd follow the WBC and be interested even if I wasn't a baseball fan. The fact that it is baseball makes it even more appealing to me.
I really don't care about the names, although I do want to best atheletes available. I'll watch because I love baseball, and I enjoy international competition. So, yeah, I care.