>>1723227Not an anime.
She is from a japanese bullet hell video game series called Touhou just like Cirno.
She is based on a special kind of youkai (japanese ghosts) called tsukumogami. This are mostly loved and hated objects which got lost or got older than 100 years and became self-aware of their existence.
More accurately she is a forgotten umbrella, a kasa-obake.
https://en.wikipedia.org/wiki/Kasa-obake http://yokai.com/karakasakozou/This following isn't canon about her backstory and just an assumption what happened:
You can say she was originally a purple umbrella of a girl which looked just like her. This girl lost the umbrella during a heavy storm. The umbrella became self-aware after lying alone somewhere outside for hundred years, because no one wanted to pick it up because of its color. That umbrella turned into a Kasa-obake, but can't remember anything besides that someone forgot it a long time ago. That kasa-obake divided it's "soul" somehow and this new part became subconscious a copy of the girl which lost the umbrella originally, but the umbrella doesn't know about this anymore. The real girl died already of old age at this time. And someday the umbrella and it's second side arrived to Gensokyo (the world of the Touhou series) and became known as Kogasa Tatara (a name she gave probably herself).