Is Jin a Korean or Japanese name?

I always thought it was a Japanese name because of the manga artist Jin Kobayashi and several anime that I have seen had a Japanese character with that name, Samurai Champloo is the most recent tone that comes to mind. But the sergeant in this movie had the name, and when I think about it I cant recall J being common in Japan while there are a few other Korean names that I can think of like Jeong that start with J.