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Not totally 100% sure about Hui and Zang, but It is a known universal truth that first and foremost, Mong and/or Hmong, is and was never a documented nomenclature is any/all Chinese historical records, history, and documents ever written, or in any scholarships to my knowledge -- even at present. That said, it a known universal truth that Miao is and has been exclusively the nomenclature of non-Chinese ethnic groups since Chinese antiquity. That truth can be found, cited, and clearly documented in nearly any/all Chinese historical documents, regardless of who, or what ruler was in power throughout Chinese history, even up to the PROC, which is why Miao was used so predominantly.
Mong and/or Hmong is a SEAsian appellation/origination near the latter 20th Century, during GVP's era/reign. This truth can be researched, clearly traced, and validated with worldly scholarships. Not hearsay, folklore, fairy tales, and wives rumorville.
Ha'HINT:
As an amateur researcher, for personal knowledge, I have studied and still studying (that is continued research) Mong/Hmong (and Miao) history etc for the past 10+ years now; therfore I am pretty sure I have a clue, or a lot of clues, as to what I am saying (NOT your typical ha'primitive ha'ignorant ha'clueless ha'idioctic HA'MUNG ha'ranting HA'MUNGINGLY ha'nonsense ) ... kekeke ...
Any/all claims that Mong/Hmong is an ethnic origination in and throughout Chinese history is pure nonsense. (NOT the people, the nomenclature.) Even our Hmong kins in China (who avow being Miao), still there today, are clueless what Mong/Hmong is and are till we spoonfed them, just fairly recently around late 1980s. This can be proven.
Lastly, most, one can even argue, the newly incepted nomenclatures of Miao ethnicities of the 55 came into existence purely out of government public assistance programs starting around the late 20th century when China become more global and worldly to better its worldwide view/tolerance etc.. Again, this can be proven. Ua tsaug ... KEKEKE ...