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.

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