饅頭 is slightly different from 馒头, even though they are based on the same idea of a steamed dough bun thing. Transliterated into the English alphabet, one is manju/manjuu and the other mantou. They even have separate wikipedia pages. If you say mantou i'll think of the Chinese version because it's the Chinese word and if you say Manju i'll know it's something slightly different i'm not familiar with because it has filling while mantou is just straight dough. It would be unwise to disregard the regional differences (i'm sure korea has their version too) so it is best to use the native word for the one you are referring to to be clear.
"naan" bread is similar to this. It is a simple food item that exist across an enormous region from central Asia to India to the Levant, and its names in each language are very closely similar. "naan" is the English transliteration of the Persian word according to Wikipedia, but you could describe it in pure English as "flatbread" just as you could describe mantou as "steamed dough buns" because that's literally what they are. The problem is that this is less clear because these descriptions can be confused for European flatbreads or buns for example which would taste quite different.
There really is little reason in this day and age not to use the native word for a country's food items because these words become commonly used so quickly in English speaking countries. The only thing you should worry about is how they transliterate it into the English alphabet. If you invited me to a "gyoza-ten," I would expect Japanese style dumplings, if you said "jiao-zi" i would expect Chinese dumplings, and if you just said "dumplings" I would still expect Chinese dumplings as opposed to Japanese or the now obscure "clootie-dumplings" from Scotland which originally gave us the word "dumpling". This bias is simply a function of WHICH dumplings the WORD "dumplings" is used most often with.