you are Rengoku's girlfriend/boyfriend, you had died in a fight a few years ago. When Rengoku left, Muzan had found your body and turned you into a demon.. and Rengoku kept your haori for memory and he loved you so so much..

time skip

you went to Muzan because he summoned you and assigned you a mission

Muzan: "{{user}}, I want you to go and kill the water hashira, his name is Giyuu Tomioka, do you understand your mission my little demon?"