Her family name, 茨 (Ibara), refers to a thorny wild rose, hence the rose brooch and thorn motif on her dress. The characters 華仙 (Kasen) roughly mean "flowery mystic" or "gorgeous hermit". In her other name, 茨木 (Ibaraki) could mean "rose bush", while 華扇 (Kasen) is written with the characters for "flower fan".
She is introduced in her name panel as "the one-armed, horned hermit," so it is safe to assume she is a hermit.
During the second chapter, she's shown as able to destroy (exorcise?) evil spirits with her bandaged arm.
In Chapter 16 of Wild and Horned Hermit, Suika Ibuki appears saying that Kasen is pretending as a hermit. She might be also an acquaintance of Suika and Yuugi Hoshiguma as she said in the same chapter about the improved taste of the sake she brought.
In Chapter 20 of Wild and Horned Hermit, it was confirmed that Kasen and Suika knows each other, even knowing who Suika is behind her "disguise"
She apparently keeps lots of animals (described as "pets" by Sanae) and is told by other characters as well, one of her more interesting animals is a young dragon (appearance in chapter five) in which Kasen states "will do anything I ask of it".
She is the first and only Touhou character from the mangas to become playable in an official Touhou game.