The characters for Yakumo literally mean "eight clouds" (but can also mean "countless clouds"), and Yukari "violet". All of the Yakumo family are named after colors. The light frequencies (energies) of the colors are proportional to their powers: Chen (orange) << Ran (indigo) < Yukari (violet). The energy of violet light is the highest in the visible spectrum, and violet light is the boundary between visible and invisible light. Red light (the symbolic color of Remilia Scarlet or Reimu Hakurei) is another boundary, but they are stronger than Chen. Fittingly, when Reimu and Yukari team up in Imperishable Night, they are called the "Boundary Team". In addition to maintaining the Hakurei Barrier, their colors form the two boundaries between visible and invisible light. In addition, the word "yukari" is uncommonly used to mean "border" or "edge", albeit with a different character. The character for Yukari, "紫," is the same character used for the name of Murasaki Shikibu, famous female author of the Tale of Genji, which is generally considered the first novel and among the greatest from Japan.
"Yakumo" also comes from the first ancient poem written in what would become the Japanese "Tanka" form:
Yakumo tatsu / Izumo yagegaki / Tsuma-gomini / Yaegaki tsukuro / Sono yaegaki wo
Definitely in keeping with the character's origin/age in the storyline. The translation into English is: "Eightfold rising :clouds/ Build an eightfold fence / An eightfold Izumo fence / Wherein to keep my bride-- / Oh! splendid eightfold fence." :This poem was attributed to the god Susanoo. Interpretations vary as to the meaning of the poem.
Relating to the above, "eight" in some cases can be read as "infinite" in Japanese. "Zero" (or "rei"), in multiple cultures, can also be seen as infinite. Both Yukari and Reimu, respectively, can be seen as having "infinite possibilities".
Yukari's name is thoroughly analyzed in chapter 26 of Curiosities of Lotus Asia by Rinnosuke. However, Rinnosuke implies at the end that there may be even more meanings hidden in it. Chapter 26 of Curiosities of Lotus Asia also reveals that Yukari Yakumo gave herself that name.
Occasionally, double rainbows form after rainfall -— there's the rainbow one usually sees (red on the top, and violet at the bottom), and another, larger, fainter one above it. The colors on the second rainbow are reversed -— red on the bottom, and violet at the top. In other words, the outside edges of the rainbow are violet —- or, put another way, violet forms the boundary between the sky and the rainbow. Thus, Yukari's given name strongly signifies the idea of boundaries.
When Rinnosuke had an iPod in his shop, only Yukari knew how to actually use it, and further knew that it was considered a trendy item in the outer world. She similarly knew about the Nintendo Game Boy and DS. (source: Curiosities of Lotus Asia #11 and #11.5, respectively.)
Because of her understanding of technology from the outside world, there are rumours that she lives in the outside world from time to time.
Marisa once stated that Yukari uses a small box to talk to her shikigami when they are far away from her, which led Rinnosuke to believe that she owns a cell phone (at least two, really). However, the 'box' that Marisa could be referring to may actually be walkie-talkie.
The outfit Yukari wears in IaMP, IN, and SWR has two groups of solid/broken lines called trigrams on the front. A solid line represents Yang and a broken line is Yin. The top trigram (☱) is "dui" or "tui" (open) and is associated with west and water. The bottom trigram (☷) is "kūn" (field) and is associated with southwest and earth, as well as Yoni Yoni (divine passage). The two trigrams together in that order form the hexagram for "clustering," "gathering together," and "finished." Sounds more fitting for Suika in a way...
More on the hexagram, the hexagram "Ts'ui" formed by the combination of "tui" and "kun" results in a meaning of gathering together to persevere towards a destination. This hexagram signifies also great wisdom which is necessary for leadership when directing an assembly together to create overall prosperity for everyone (for example a ruler). Yukari herself can be seen as an overseer of Gensokyo. Her ability to create borders would definitely give her the ability to bring everyone together (perhaps by force) while maintaining the harmony of the "created" world. Maybe this design was a critique on her abilities?
For some reason, Yukari's appearance in spell card 222 in Imperishable Night is different from other characters. Instead of using the new image in Imperishable Night, a modified image from Perfect Cherry Blossom is used (she has blue ribbons instead and dress is red). What is more strange is that the background used in the spellcard, which is also from PCB, uses Yukari's original cut-in image with red ribbons. Yukari's sprite in StB also sports blue ribbons.
She is the only Phantasm boss in the series.
There is a train service in Japan called Yakumo. In Scarlet Weather Rhapsody, one of Yukari's spell cards spawns a train to mow her opponent down.
One of her alternate palettes in Hisoutensoku is based on her best friend, Yuyuko.
Another of her palettes in Hisoutensoku bears resemblance to Kanaria, from Rozen Maiden.
Her ability is manipulation of all boundaries. In Japanese, it can be pronounced as "スキマ(Sukima)". It sounds same as "Gap, boundary", but also sounds very similar to "Scheme(Sukimu in Japanese pronunciation)". It is intended for dual meaning of her ability itself and her characteristic.