In many fan-fictions, she is regarded as a familiar of Patchouli. In those fictions, she works as a librarian and a personal servant of Patchouli. Some of those fictions also portray Koakuma as originating from Makai.
Similar to how the Scarlet Devil Mansion has many fairy maids, some fans imply that there are multiple Koakuma as opposed to just one.
In many fictions, she is described to be very obedient, steady and good-natured, on the contrary to ZUN's official profile. This personality is acknowledged before ZUN replied to the question, and it is one of exceptional example of a fan-made profile which is accepted by a large majority (but not all fans).
After ZUN's reply, some people described more impish and mischievous Little Devil in their fan-fictions. Today, various Little Devils exist in fan-fictions: Obedient and steady, impish and mischievous, or hybrid of them.
Koakuma is sometimes drawn by fans having a pair of black, bat-like wings on her back to match the ones on the sides of her head.
Some fans have given Koakuma the catchphrase "Koa." In extreme cases, she's shown as being able to speak only this phrase.