I did not realize that the (oldest) named clans where named after the zodiac until I saw this episode.

It was said in the episode the first 12 clans where named after the zodiac and the latter ones have unrelated characters, and they were commonly divided along that line as old / new, La clan being one of the new ones (probably the most prominent) and there are others (just not explicitly mentioned in the story so far).

It is interesting that the horse clan uses the animal character (馬) and not the zodiac character (午). This is the only exception. I guess it was probably one of the original 3 vassals who helped establish the nation.

It was also mentioned Gyokuyou’s clan would most likely be raised to named status with the character Gyoku (玉, Jade) once she became empress consort.