The characters for Komeiji literally mean "ancient and pure/bright earth". Satori isn't written in kanji, but it's pronounced the same as "satori" (悟), which means "enlightenment, profound understanding", as well as the name of her youkai species.
With the exception of her first spell card, all of Satori's spell cards are based on, if not directly stolen from, those of the player's partner.
Similarly, it has become common in fan art to break down the kanji of Satori (悟) into its component radicals (小五口) and add the katakana リ, spelling out "shougorori", read as "fifth-grade elementary student loli". Her apparently small stature in her portrait seems to add to this. It is thus not uncommon to see her depicted wearing a Japanese elementary-schooler's book satchel on her back.
Satori and Koishi's design may have been inspired by the 1939 painting by Kahlo titled "The Two Fridas". The subject is essentially two identical women (sisters/clones/twins...) with visible hearts and external arteries that seem to connect and wrap around their shoulders and arms.
Satori is currently the only Touhou Windows character that appears before her subordinate is introduced.
If her and Koishi's color schemes are inverted, they will both somewhat resemble each other.
At seventy-six cards total, Satori has more spell cards in a single title than any character in the series (one spell card of her own, plus three cards from the player's partner, across four difficulties). The only character who comes close is Kaguya Houraisan, with forty cards total.
Using spell cards from such harder bosses, (Yukari Yakumo and Suika Ibuki) Satori is one the hardest 4th stage bosses in Touhou.