Should, "romaji", a loanword from Japanese, be capitalized because it is ultimately related to "Rome", which is a proper noun?
I came across Should capitalization be preserved in loanwords? , but "romaji" is usually not written in romaji in Japanese. For example, it's written ローマ字 in the Japanese edition of Wikipedia. How heterological!
In English the convention is to capitalise proper nouns. If romaji were a proper noun I would certainly capitalise it, however, in this case it is only related to a proper noun. Here there is a grey area where some words are inconsistently capitalised, for example, anglophone. It seems in this particular case convention is not to capitalise, as seen with the similar word kanji.
The word romaji is a noun, and it is not directly derived from a proper noun. So, it is not typically capitalized (as attested, for example, in the Oxford English Dictionary). It is different from, e.g., the adjective Roman (related to the modern city of Rome, or to the ancient Rome).
Kanjidict gives the translation as lowercase romaji:
For the benefit of those who don't know what this word means, it is a foreign word rendered in Japanese using Roman letters.
"Romaji" in Japanese is not derived from Rome, the city (per se).
It IS derived from "romanization," that is the use of the "roman" alphabet to describe Japanese sounds. But "romanization" is in the lower case, and therefore, so should "romaji."
