It is said that the letter '興' in Okimoto (興元) was after his older brother Tadaoki (忠興) HOSOKAWA, and the letter '元' was after Mototsune (元常), the foster father of Fujitaka.
興元の興の字は兄・細川忠興からのもので、元の字は藤孝の養父・元常に因むといわれる。