The surname Hosokawa originated from the fact that the family settled in Hosokawa-go, Nukata County, Mikawa Province (presently around Hosokawa-cho, Okazaki City, Aichi Prefecture) in the 13th century of Kamakura period.
細川という名字は鎌倉時代13世紀に三河国額田郡細川郷（現在の愛知県岡崎市細川町周辺）に土着したことに由来する。