I think martial artist is the only other name for monk you could use. It does still implying Asian fighting styles, but I think with the rise of MMA fighting that it's going to be the generally preferred term in our culture going forward.
Dragon Quest games have soldier and fighter for fighter and monk, respectively, and I think that's a better scheme even if you used warrior instead of soldier. But it's not going to work for D&D. You can't rename fighter of all things when you're 50 years deep and it's the OG of OG classes of the entire thing.
Pugilist is... fine, but like boxer or brawler it's not really an all-encompassing term. Even if the class eliminates the explicit Asian trappings, it's not really including the light weapon use that the class is still likely to include. Besides, we have more than enough trouble with people mispronouncing paladin without introducing dog breeds to the conversation.
