It is generally assumed by the majority of fans that Koakuma is Patchouli's summoned familiar and personal assistant, as she is rarely seen outside of the library unless accompanying the magician, and served as Patchouli's midboss in EoSD. Because of her strong physical similarity to Morrigan Aensland, she's also frequently depicted as a succubus in fanworks, despite ZUN calling her more of an imp and her exact species being unknown.
Unused sprites in the EoSD game files include a possible "EX-Koakuma" with violet hair and a purple arcane aura, which might have been meant to appear alongside Patchouli during the Extra Stage midboss fight.
Person: long hair, red hair, red eyes, wings, head wings, demon wings, bat wings, demon girl, demon tail
Outfit: shirt, white shirt, collared shirt, long sleeves, black vest, vest, necktie, red neckwear, skirt, black skirt, skirt set, black dress, layered clothing
Accessories: book, holding book, bookshelf, voile