Shouldn't have taken this long to click (probably distracted by the art lol) but with the talk of taking over her body and "living a life that matters" I'm realizing "Butterfly Dream" is most likely a reference to Zhuangzi's self titled work, which tells of a man who dreamt he was a butterfly and became able to fly and do all sorts of things he couldn't as "Zhuang Zhou" the man.
Interestingly enough, there is not a consensus on the theme of this story. Some interpretations say it's a chaotic tragedy of fugue and identity loss, with Zhuang Zhou eventually losing his ability to understand if he's a man dreaming of being a butterfly,or a butterfly dreaming of being a man, and can no longer perceive his self.
The more I type that out the more I'm actually positive that dusty piece of required reading in philosophy class (yes I'm bitter) is the thematic inspiration for this series.
Also, and this is just my personal opinion, and native English speakers are free to correct me, but it's probably less weird to call her Miss or Lady Meng than "Butterfly Dream", even though nushi and xiaojie aren't used the raws. I used Meng instead of Die since the character for Meng was the specific inspiration for Zhuangzi