can you use Korean or Chinese letters in your name on league or will it show up as boxes?

I think name will show up fine, only when you chat using them will show up as boxes I think.

Correct if wrong.

Both. In game they show up but they don't in the loading screen for some reason.

At least this has been my experience.

http://www.lolking.net/summoner/na/245353/잘%20못 Has Korean characters in his name.