I was at school with a girl who changed her name, she started using her middle name instead of her first name.
It was fairly straightforward, she just told people she was changing her name and could we call her X instead of Y. She had to remind people at first but it was surprising how quickly people forgot the name she used to use.
She went from sharing the name of a loud and fairly annoying soap opera person to having the name of a slightly out of fashion singer and actress.
But the soap opera name was very obvious as the only well known person with the name, the actress/singer name was more general and other well known people shared it as well.
She was teased for the soap opera name, a few people commented with "oh, like X, the singer" when she changed it. I wonder if your daughter is the same, if she's being teased for one name and that's why she wants to change it, rather than because she really hates it for other reasons.
I recently bumped into the girl from school and she now wishes she'd stuck with her first name, it's become a bit more cool and edgy and the soap opera character is long gone. But she said she can't change back now, once was enough.