Because of his position of power and the fear that he inspires, it is forbidden for demons to speak his name, and those who do so are punished severely.
The curse prevents Muzan's name from being spoken aloud, and any who do will meet a horrible demise. One demon, Susamaru, faced this reality when battling Tamayo. Susamaru accidentally shot Muzan's name aloud, attempting to defend his honor with her mind clouded.
As Susamaru desperately attempts to silence her, Yushiro notes that Tamayo is using her Blood Bewitchment: Magical Aroma of Daylight ability on the Demon to get her to say Muzan's name, which she does, and Muzan's curse then suddenly begins to break out from inside her.
The only Demon he despises the most is the Upper Rank Two: Doma. It is quite a shocker that the second most potent Demon in the Demon Slayer is not Muzan's favorite.
It is unclear if the curse branded to her by Muzan got lifted or not, but she can't speak a word after turning into a demon, and always has a muzzle in her mouth. As Nezuko can't speak Muzan's name out loud, she can't be affected by the curse.
Muzan Kibutsuji (鬼舞辻無慘, Kibutsuji Muzan) is the main antagonist of the Demon Slayer: Kimetsu no Yaiba fantasy action manga and anime series. Muzan is the powerful Demon King, who has the ability to inject his victims with blood that allows him to convert them into more demons.
Enmu was one of the demons serving under Muzan, the first of his kind as well as the Demon King.
With his blood, Muzan can turn others into demons and seems like an unstoppable foe. However, the demon king seems to fear one thing: Tanjirou's hanafuda earrings. A look into Muzan's past reveals that only one man ever came close to killing him.
Doma is always smiling and acts very friendly, but this cheerful, caring nature is simply a facade. He states that he cares for his fellow Upper Moons and even cries when he learns that Akaza died, though, in fact, he doesn't feel anything for them. Even when he was human, Doma didn't feel any type of human emotion.
Akaza is an upper-rank-three Demon and one of the most faithful minions of the Demon king Muzan Kibutsuji.
Yushiro is in love with Tamayo and is willing to do anything to protect her. He finds Tamayo very beautiful. He is very obsessed with her and will attack and insult anyone who comes near her but him.
Anne was originally planned to be Muzan`s older sister, who died by the hand of a Demon Slayer but that idea was scrapped, as the author knew practically nothing about Muzan`s early life. Instead, Anne became his wife, by which he had two children.
Yushiro (愈史郎) is a Demon that is shown to be close to Tamayo, Yushiro also allies with the main protagonist, Tanjiro Kamado in the Kimetsu no Yaiba (Demon Slayer) series. Yushiro has been in love with Tamayo for over 200 years, and is willing to do anything to protect her.
As for how she removed the curse, it wasn't explained. Cause Nezuko somehow freed herself from the curse, so she's no longer under Muzan's control, so since Muzan can't control her, he can't kill her.
EDIT: I forgot that we got to hear Enmu say Muzan's name, probably because the Upper Moons were much more present in the series and for longer than the Lower Moons, neither Enmu or Rui really being in the series for that long, compared to most if not all of the Upper Moons.
Muzan was born in Japan's Heian era, to a constant struggle to survive on account of his frailty. His heart stopped multiple times in his mother's womb, and when he first entered the world, he was deemed stillborn, having no pulse and not breathing.
However, in truth, as revealed after her death, Muzan sees Daki as a tool to keep her brother, Gyutaro, in line, deeming her to be the main reason why the "true" Upper Rank 6 was killed and in truth does not think highly of her and deeming her as someone not very intelligent.
Akaza. Because of his desire to become stronger and Doma's strength allowing him to surpass himself to become Upper Two, Akaza harboured an intense hatred of Doma. Doma, as apathetic as he is, considered him his "best friend", seemingly ignoring the contempt Akaza possessed.
Yet an official Demon Slayer "fanbook," written by the manga's creator, Koyoharu Gotouge, revealed Muzan doesn't really like Upper Rank Two demon, Doma. As Lower Ranks Six, Four, Three and Two can attest, Muzan is not averse to eliminating demons he doesn't care for, even if they're Kizuki.
Does Muzan have a favorite demon? Despite the fact that Muzan. is always shown to have disdain for his creations, Muzan does in fact have a favorite. On that list is Naki, made due to a convenient blood demon.
14) Muzan Kibutsuji (over 1000)
Being a demon, Muzan is capable of living for many, many years. However, unlike other demons that have aged over hundreds of years. Muzan is well over 1000 years old.
1) Kokushibo
Kokushibo stands at Upper Rank 1 in the Twelve Kibuki. He is the only demon to have a breathing style in the Demon Slayer series. In fact, Muzan views him as more of a business partner and one of his closest allies.
These neutral features, as well as a slow, drawling voice, can make Enmu's gender seem ambiguous. RELATED: Who Is Upper-Rank One in Demon Slayer? Despite that, Enmu is, in fact, male -- and one with sadistic tendencies.
Throughout his life as a demon, Akaza never felt any sort of awe, hatred or respect for Muzan, instead viewing him simply as someone who gives orders and himself as someone to carry them out. Muzan became fond of him, due to his loyalty, will to become stronger and gave him special permission to not eat women.
Muzan then decided Enmu was worth keeping alive so he can attack the demon slayers and gave him more of his blood making him stronger, promising him more blood if Enmu can kill Tanjiro or the Hashira. Enmu's body could hardly process so much new strength from his upgrade and he almost died.