Before I begin, I speak and read Chinese, I also teach Chinese Martial arts,
if someone wants to teach Chinese martial arts and not use Chinese terminology that is their business, if someone asks my opinion as a Shifu and who speaks and reads Chinese if someone does not use Chinese terminology in their class what I think,
I would think it is odd, and maybe think they do not understand the art they are teaching well enough, if it is a Chinese martial art I practice and I happen to see, feel the technique and still see they use some weird name for it, I might offer them the Chinese terminology, ask why they do not learn the Chinese terminology for it,
if a Shifu still declines I most likely would not take them to serious as a Shifu of that Chinese martial art in my opinion.