In Japan, the Japanese Ministry of Education (now Japanese Ministry of Education, Sports, Science, Culture, and Technology) issued guidelines on how to transliterate Japanese words into the "Roman" alphabet.
There are actually two systems in use: the government-approved Kunrei-shiki, and the more widely-used (and useful) Hebon-shiki. The Kunrei-shiki system of romanization is taught in schools. The Hebon-shiki is the system everyone uses when they realize the Kunrei-shiki is inadequate and produces unintentionally bad results for English speakers. For example, the "Fuji" of Mt. Fuji would be rendered as Huzi in the Kunrei system. The railway and subway systems notably use the Hebon-shiki, as do most other industries. Even the Japanese government uses the Hebon-shiki in passports and other documents. But for some reason the Kunrei-shiki persists in the education system, despite everyone abandoning it once they reach university age.
I think most countries must have something like a "Ministry of Education" which promulgates certain official English spellings of native words and names. In the absence of such a body, my gut feeling is that it is the English speakers themselves will eventually form a consensus of how certain words are to be spelled, and those spellings take root until/unless they are forcibly changed by some official mandate. Legacy systems die hard, though.
