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
One of these is clearly not like the others. Interestingly Zoro’s birthday is in November and Momo’s name and sword have ‘heaven’ connotations. Any significant characters we know born in May? Kurozumi clan not having the moon character makes sense given that Orochi’s ancestor apparently betrayed the Kozuki.
@Light D Lamperouge @Cyrus the Cactus