I did this little research for a reply to another post but I thought I might as well give it its own post. Sorry if many people already did / know this. If I made any mistakes, I welcome corrections in the comments since this isn't based on professional research.
Most of my sources are at the very bottom.
So, an explanation of 九条 (Kujō) was easy to find through Wikipedia:
I assume her surname is a reference to the second entry, the Japanese regent house.
An explanation for Sara was a little more difficult to find, as my Japanese keyboard couldn't find the right Kanji suggestions for さら as one word. What I could find was that both 沙* and 娑* are names of a plant called Shorea Robusta or, more commonly called, Sal Tree.
The first Kanji of both writings of the tree's name are very similar to the one shown in the image of Kujō Sara but they're not the same, so I wasn't satisfied yet. That's why in the next step I searched for さ and ら's Kanji separately. That's how I found an entry for 裟* on a Japanese word search website called kotobank that goes through different Japanese dictionaries. I know Google Translate isn't perfect but using it for the page, I got that 裟* is just another way to write Shorea Robusta / Sal Tree in Japanese.
This is the tree, whose blossoms are rather unique but still pretty:
Both picture sources resulted in 404s, so I can't give them here.
Since tree, blossom and fruit names for people aren't unusual in Japan, this seems like a reasonable meaning to infer.
Maybe related:
The sara in Basara (婆娑* or ばさら) can be written with the same Kanji the Sal tree's Japanese name can contain. Some of you might know the word from the gaming series 戦国BASARA (Sengoku Basara) or the other gaming series simply named 婆裟* (Vasara).
The word Basara originated in the Japanese Middle Ages and was apparently a social trend that disregarded social norms and favoured flashy clothing
At first this reminded me of Visual Kei, but looking up some famous Japanese social and fashion trends, this seems more like a regular occurrence >>> https://www.airyhair.com/blog/top-8-insane-japanese-fashion-trends/
Maybe once we learn more about Kujō Sara, this will prove to be part of her story.
Of course this could also be totally unrelated non-sense thought up by an uneducated Westerner. Kinda like an English-learner might see the words house and mouse and think they're related just because they both contain the part ouse.
Kinda related but still off-topic:
Apparently there's also a character called 九条 サラ (Kujō Sara) from a Japanese early-2000s video game called "Innocent Tears" (イノセントティアーズ). The game was fully voiced and Sara was voiced by Okada Junko. Along other high-profile seiyū, one of my favourites, 緒方 恵美 (Ogata Megumi), also voiced a character in that game.
If you don't recognise the name, maybe you'll recognise some of her voiced characters:
(Among others: Ikari Shinji from Neon Genesis Evangelion, Sailor Uraaa- can't say that name here from Sailor Moon, Kurama from Yū Yū Hakusho, Tsukishiro Yukito from Card Captor Sakura, Amada Ken from Persona, Naegi Makoto from Danganronpa 1)
(Komaeda Nagito from Danganronpa 2, edited version by KitKat_Caffiene >>> https://www.reddit.com/user/KitKat_Caffiene/)
(Yugi Amane and Tsukasa from Toilet-bound Hanako-kun))
This was fun to research. I hope you found my theories interesting to read. And again, if you have corrections to what I said from a more Japanese-proficient perspective, please leave them in the comments! And of course, I'm open to any other theories you might have.
Other sources:
https://en.wikipedia.org/wiki/Kuj%C5%8D (EN Wikipedia entry on Kujō)
https://kotobank.jp/word/%E8%A3%9F%E7%BE%85-1759784 (kotobank's entry on Sara / 裟*)
https://kotobank.jp/word/%E5%A9%86%E5%A8%91%E7%BE%85-600893
(kotobank's entry on Basara / 婆娑*)
https://www.japanese-wiki-corpus.org/history/Basara.html
https://ja.wikipedia.org/wiki/%E3%81%B0%E3%81%95%E3%82%89
(JP Wikipedia entry on Basara / ばさら)
https://ja.wikipedia.org/wiki/Innocent_Tears_(%E3%82%B2%E3%83%BC%E3%83%A0)
