I have no problem with Hmong vs Mong.
What I don't get is who the hell came up with either one? The English letters that best pronounce "Hmoob" are "Moan".
Just read it out loud.
Hmoob.
Moan.
Hmoan!
As in English language, Hmong must be Hmong, not Mong, it doesn't matter you are green or white Hmong.
In other languages, Hmong can be written differently by their way of writing or speaking, but in English, it must be Hmong. It's like we called Chinese as "Suav" in Hmong language, as well as the Chinese people might call themselves differently too.
Whoever created Mong to differentiate between White and Green Hmong is considered a betrayer.
Remember, Hmong had a story about when we lived in China, we had no last name at all and we were very united. The Chinese can't do a thing to us, so they created last name to divide us. That's probably why we have many identical last name like them.
Whoever refer me "Hmong" as a White Hmong, I will tell shut up and f*** yourself. Sorry a little

Hmong is Hmong, and will always be Hmong, including the Hmong in China, Laos, Thailand, and many other countries.