Her "Yamaxanadu" title is considered to be a combination of Xanadu (an ancient palace of the Mongol warlord Kublai Khan, which was later used as meaning a "Pleasure Palace" in a poem by Samuel Taylor Coleridge) and her status as Yama, and can mean something along the lines of "Yama of Paradise".
In fan art, her name is also shortened to Yamada (山田), a pun on "Yama da!" (It's the Yama!) Yamada is a very common Japanese family name, the Japanese equivalent of being called, for example, "Smith" in American English or "Pérez" in Spanish.
Based on this, "Eiki Shiki" (using English name order) would be her Romanized name. "Eiki" means "reflection princess" and "Shiki" means "four seasons".
Though "Yamaxanadu" is her title, though it is sometimes mistaken for her last name. This can result in jokes making fun of the excessive length of her name.
Common nicknames for Shikieiki are 「えーき様」 ("Eiki-sama").
In Shikieiki's Spell Cards, the background is "The Last Judgment" by Michelangelo.
As explained in PMiSS, she carries her rod with her everywhere. She even appears to carry it in her character portrait.
The "Shikieiki" spelling has recently garnered more fame than the actual in-game (PoFV) spelling of "Sikieiki".
She is sometimes depicted as a midget or even a baby compared to Komachi, but she's actually almost as tall.
A possible reason behind "Loli Yama" is to artificially create extra contrast with Komachi and play up the breast envy angle.
Based on her conversations with the many playable characters in PoFV, she is seen as a compassionate individual, though her conversations with Komachi can seem quite harsh. Despite all this scolding, however, Komachi remains a slacker.
She tells Yuuka Kazami to "scare humans" like a regular youkai and tells Reimu Hakurei to "exterminate youkai more." Both of these cases can be simplified to "do your job" and it showed she does not discriminate between youkai and humanity.