The five clan names are as follows:
風月 - Fugetsu - wind moon (can also mean nature’s beauty)
天月 - Amatsuki - heavenly moon
霜月 - Shimotsuki - frost moon (can also mean 11th month)
雨月 - Uzuki - rain moon (can also mean 5th month)
黒炭 - Kurozumi - black charcoal