As the head maid, 「メイド長」 or "maid-chou" or "maid-boss" is the common title used to address her among fans. Another common nickname is 「さっきゅん」 or "Sakkyun."
Another recurring joke with fans is the idea that Sakuya pads her chest to make it seem bigger than it is and goes to great lengths to hide this secret, even from Remilia herself. The origin of this joke was due Sakuya's portraits in Immaterial and Missing Power, which for some reason showed her with larger breasts than were seen in all of her other ZUN-made portraits (with the possible exception of Embodiment of Scarlet Devil). Thus, 「ＰＡＤ長」 ("Pad-chou") has become a popular phrase that is frequently seen with 「メイド長」... but be careful when you try to use it. There are many people hating that nickname. Thus, another common joke is to depict Sakuya as knifing everybody who says that, making Sakuya a Touhou version of the Candlejack meme.
In fanworks, Sakuya is sometimes seen with nosebleeds in the presence of Remilia or Flandre.
In some fanworks Sakuya stabs Meiling in the head out of jealousy, for having bigger breasts than her.
Or sometimes for sleeping during her work as Gatekeeper.
In some fan-produced works, Sakuya is depicted with puppy ears and a tail (commonly called 「犬咲夜」 or 「いぬさくや」 or inu-Sakuya), which is probably a reflection of various characters referring to her as Remilia's dog.
Sakuya is sometimes depicted as a mass murderer due to multiple jokes. The most popular of which are her knifing anyone that mispronounces her name, says the word "pad," and knifing Meiling because she is sleeping on the job or just because she has larger breasts than her.
Some fans speculate that, though listed as being human in all works, Sakuya may be at least part vampire on account that she works as a servant for two full vampires. The speculation has no official works backing it up, but it would explain multiple fan depictions of Remilia feeding from Sakuya and Sakuya remaining how she is because she is already part vampire. It also explains how Sakuya's eye color changes when she is angry or frustrated (they go from navy blue to red), as when she becomes upset, the vampire bit of her comes out in hostility.
Many fans speculate on how Sakuya came to be Remilia's head maid.
One theory is that Sakuya was a vampire hunter who originally came to the Scarlet Devil mansion to kill Remilia. Upon her defeat, Remilia convinced her to work for her and Sakuya grew attached to the vampire over time. This is one of the most popular theories.
Another is that Remilia found her as a child and raised her.
Some fans think Sakuya is a Lunarian due to the scenario in imperishable night with Eirin.