Youmu is often called "Myon" by fans, as she inexplicably asks Yuyuko why she is present at such a "myon" place in the PCB extra back story. ("Myon-na" is a portmanteau of "hyon-na" (unexpected) and "myou-na" (strange).) But, in the western fandom, it's her phantom half called Myon. It's also occasionally referred to as an "option" (like the ship accessories in Gradius), but this is less common.
The characters for Konpaku mean simply "soul", and Youmu something like "bewitching dream".
Although both "Kon" (魂) and "Paku" (魄) are "soul", their elements are different. "Kon" stands for a mental soul, which is separated from a body as soon as a human dies and ascends to Heaven. "Paku" is a physical soul which remains in the body a few days and goes back to the Earth. In this case, "Kon" is Youmu's phantom half, and "Paku" is the human half. The entire Konpaku family is comprised of half-phantom half-humans, as noted by Perfect Memento.
In Phantasmagoria of Flower View, Youmu's name is written in Roman letters Japanese style, with her surname first, during pre-battle conversation with her, even though every other character in the game with a Japanese name has their name romanized western-style, with their given names first. This is one of several typographical inconsistencies in the game (another being the inconsistent spelling of Aya's name).
Because of Youmu's spellcard "200 Yojana in One Slash," she is said to be capable of striking at speeds most would consider physically impossible (200 yojana can be a distance anywhere from 1,320-3,000 kilometers or 825-1,875 statute miles in length). In order to cover that kind of distance in the split-second a typical sword slash takes to execute, she would have to be capable of moving at far beyond hypersonic speed; her slowest sword slashes have been calculated to move at speeds in excess of Mach 70 (70 times the speed of sound, or 53,200 mph/85,120 km/h at sea level), fast enough to circle the entire Earth at the Equator in less than half an hour and around three times the speed required to orbit the Earth, for reference. One doujinshi (Touhou Kaidan Seven #3) went into far too much detail trying to work out the specifics of this, and determined that her theoretical top speed was approximately one quarter of the speed of light...
Her theme song is titled "Hiroari Shoots A Strange Bird ~ Till When?", named after a story in which a warrior named Hiroari slays a youkai known as the Nue. This is a pun on the storyline. The "strange bird" is a Nue, also called the "Itsumaden", since it makes this cry near unmourned corpses, meaning "How long (will this corpse remain unattended)?" Judging from the story of Perfect Cherry Blossom, the heroine plays the role of Hiroari, Youmu is the Nue, and the corpse is probably Yuyuko Saigyouji. (See also Flandre Scarlet and Yukari Yakumo.)
Ironically enough, considering her species, Youmu is afraid of ghosts, as shown in Imperishable Night's Extra Stage. After defeating Fujiwara no Mokou, Yuyuko pretends there is a ghost under a tree, earning a terrified shriek from Youmu. It is a wonder why she doesn't cower away from Yuyuko, whom herself is a ghost.
It could be that Youmu has grown used to Yuyuko's presence for a long time(possibly as long as she can remember), or that before his disappearance, her master Youki, casually introduced her to Yuyuko.
Youmu seems to have some knowledge of Chinese legend and history because of her particular win quote against Meiling, in which she asks why the latter does not wield Guan Yu's Green Dragon Blade. By the way, women didn't use polearms traditionally in Chinese martial arts. Youmu said that she's only heard about them in stories, so this misinformation is likely on purpose.
In the game "League of Legends", there is an item called Youmuu's Ghostblade as tribute to Touhou.