The characters for Saigyouji literally mean "West journey temple", and Yuyuko something like "Secluded child" or "Ghostly child." 'yuyu' (or 'yuuyuu', as in Yuu Yuu Hakusho) is reportedly the sound a Japanese ghost makes.
She has more Spell Cards in Ten Desires than is usual for a Stage 1 Boss in the Touhou series; in fact, she has more Spell Cards than the game's Stage 2 and 3 Bosses.
She is the only Stage 1 Boss, as well as Nazrin who has a purpose in the plot in Ten Desires. However she does not exactly have a role in the plot like Nazrin but rather being blamed for the incident but does know the incident herself.
Being re-introduced in Ten Desires, she strangely did not receive a remake on her sprite which stands out the most among the other Ten Desire cast's sprites.
Yuyuko, along with Toyosatomimi no Miko, is the only final boss whose final spell is not immune to spells.
The name Saigyouji comes from a famous Japanese poet, 西行 法師 (Saigyō Hōshi), who lived in the late Heian period and the early Kamakura period. He passed away in a temple, which is why the character "寺"(tera) is added (in this case it is read "ji" although this character is usually read as (tera).
According to ZUN, Yuyuko looks like a pure, innocent girl who knows nothing, but in fact she knows everything and pulling the strings from behind(Usually using Youmu). In other hands, Yakumo Yukari pretends to be a perfect mastermind who control everything, but she is not invincible, nor omniscient.
She is one of the few characters who revive (along with Eirin, Kaguya, Tenshi and Suwako) after being defeated the first time.