some odd replies here. At the end of the day she is entitled to think its old fashioned or dislike it if she wants OP, your opinion is your own, you aren't the authority on what is or is not a perfectly nice name she should be happy with. Maybe it is uncool where she goes to school? I assume she feels that its old fashioned compared to everybody else's at school and therefore makes her stick out or is uncool and feels worried about that.
It might be a phase or it might not, i would try to discuss with her whether she feels alienated at school etc and work on her self esteem with her rather than just arguing back that she is wrong and the name is beautiful and wonderful and meaningful. It is ultimately just a word.
There is no point wondering whether its a phase or not or deciding it is because time will tell won't it, nothing else will and nobody on the internet will.
I would also be honest with her that she can change it at 16 if she does want to, you will just have to manage your disappointment if she does; she is her own person.
I've always hated my name, and middle name. I pretended i didn't have a middle name in school, forgot about it all a little bit when i was old enough to change as couldnt be bothered and then finally changed the whole lot a few years ago and wish i had just done it sooner. My given names just did not match with who i felt i was, and i hated the rhetoric of my mother going on about having "given" me that name and so that's what it was. She too was awfully offended when i changed, suggested i had broken her heart and rejected her and must not care about her.
None of that is or was true, it had nothing in the slightest to do with her but she chose to believe that and i eventually went NC because of her endless guilting, comments about how ungrateful i was for the name ( foe goodness sake).