She is commonly depicted with long red hair and red eyes, bat wings on her head and (usually) on her back, and less frequently a demon tail. Her usual attire is either a black dress or a skirt set comprised of a skirt, vest, dress shirt and a necktie.
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.