It shouldn't really bother anyone. If anything, all Hmong-American people should come together and agree that we should all take a European first name if you don't have one, and change our last name spelling to better reflect what our surnames really sound like, as well as making pronunciation easier for non-Hmong people.
For example, Yang? Why not change it to "Ya"? Why not change the writing of Moua to Mua (which I have seen, like Yia "the Bull" Mua, RIP).
"Hi, I'd like to speak to (looks at paper)...Chris Ya, please." Certainly much easier for a non-Hmong, rather than to fumble with calling to speak with Toua Xiong. "Hi I'd like to speak to...Tow, Tow-a, Zi....ong?" And that would actually be commendable if a white or black person nailed it the first time. Most likely, it would come out something silly like "Too Shing" or "Tao Shine".
Bottom line is, your surname is written in Romanized form as best as the social workers and government could when they were getting ready to ship Hmong refugees over there. The fact that you would change your legal last name shouldn't mean anything. Even if someone decides to completely remove their surname so that it no longer includes a 18 clan surname, big deal. Maybe they don't want to associate with their clan any longer. Maybe they don't want to be tied down by ideas that if you're a clan name, you are bound by anything and everything any person of that last name does - Chai Vang, anyone? I can guarantee almost any white person sees that Vang surname, they ARE thinking if you are related to Chai Vang the cold blooded murder may god have mercy on his soul.