From Japanese 敏 (min) meaning "agile, quick, alert; sensitivity", 民 (min) meaning "people, nation, subjects", 明 (min) meaning "bright, light", or 眠 (min) meaning "sleep, die, sleepy". Other kanji or kanji combinations can form this name as well.
From Egpytian mnw literally meaning "established one", from mn "to establish". Min was an ancient Egyptian fertility god, often depicted as a human male with an erect penis and an upheld left arm holding a flail.