The criterion that determines a person who is professionally trained in philosophy and does philosophical research, to be either a western or eastern philosopher is not clear to me. Suppose, we have a person from Asia(which is traditionally associated with eastern philosophy), who knows nothing about eastern philosophy(and perhaps rejects it) and works on analytic philosophy, developing on the ideas of Hume, Wittgenstein and Russel, do we call him(or her) a western philosopher or an eastern philosopher?
If you work in Eastern philosophy, you're an Eastern philosopher. If you work in Western philosophy, you're a Western philosopher. It doesn't have anything to do with your identity, although it obviously once did. Jaegwon Kim, for instance, is Korean and considered a Western philosopher. Alan Watts, on the other hand, was British and considered an Eastern philosopher (not sure if he was really a philosopher, but this isn't my area and he's the only one I could think of).