My DD's name is Lily, she is 17 now and it is her. I can't imagine her being named anything else now.
But when she was born I went through so much angst about her name during that hazy, slightly manic, sleep deprived post-birth period. Names grow on children as they, themselves, develop into the unique individual that they are.
New born babies are so full of potential and possibility, that we, as parents can feel the enormous responsibility of "imposing" an identity upon them in case it is the wrong one. When Lily was born I was so worried about the name creating her, when in fact, it was my DD whose own unique individuality, personalised the name from being a mere word, into an unique part of her entire being.
Sometimes, a name given to a child will turn out to be a poor fit, but in those cases a shortened version, the use of a middle name, or creating an entirely new name altogether will mean an individual's name will evolve with the person.
So, a convoluted post to say don't worry, and that Lily is a lovely name! Let go of the preconceived notions of what the name "Lily" is in your mind knowing that your daughter will make the name "Lily" her own and, as she becomes her own person, you will only associate the name "Lily" as being that of your own beautiful daughter.