I honestly wouldn't care. If my daughter changed her name I would be surprised, as it's a very pretty (but still 'normal' name,) Think Lauren, Hannah, Emily, that sort of name. 
I do have to say also, that I have known AT LEAST a dozen people who used their middle name OR a 'pen-name.'
Eg, I discovered my auntie Joyce's real name was Mildred, when I was about 18, and Joyce was her middle name.
My BFF in my childhood/teens has a dad called John and I found out his real name was Joseph when he died (I was 23 by then!)
My husband's brother is called Peter but has called himself Steven since he was about 8! (Found this out about 6 months into dating DH.)
I found out my grandad's brother Fred was actually called Percy when I was about 12! Fred didn't even feature in his name at all! He just decided that was his name when he was 10!
And my DH's nana was always known as Penny, even though her name was Prudence, (because she hated the name Prudence, and said it sounded like the name of a cow!)
There are many more!
As a few people have said, your daughter may even change her name back eventually.
There are worse things she could do!
Bronwen is a nice name by the way! I can understand a teen not liking it though.