He was originally designed to be much more East Asian-looking:
However, it appears Bungie opted out of that in favor of making him a much more racially-mixed character; given Halo takes place 500 years in the future, notions of race are pretty different and most extraterrestrial colonies are incredibly "diluted," for lack of a better word. There are some characters with real, "definitive" races, such as the Chicago-native Sergeant Johnson. Even then, though, Bungie typically made it a point to establish that things have changed pretty significantly on Earth even though locations still retain their namesakes; Chicago is now the Greater Chicago Industrial Zone, which is a massive urban sprawl taking up most of the tri-state area in what were formerly Illinois, Wisconsin and Indiana. Said sprawl is actually a city-state with a government separate to that of the "United States," and the US, in turn, has had its remnants align with Mexico and Canada to form the United North American Republic. Backstory even suggests that another American civil conflict (Only the "political remnants" of the US joined the UNAR, while the American Civil War is referred to as "the
first American Civil War" in one of the novels) split up the Union further.
I'm going off on a bit of a tangent, though; Jun's hometown is named after a present-day Russian city, and his voice actor is of South Asian Indian heritage. I think it's safe to say Jun's racial identity is probably the most ambiguous or "diluted," with regards to the modern-day social construct. Kat, by comparison, comes from the town of Monastir (Russian for "monastery," on the same planet as Jun) and has an Israeli VA.