Wow - that's really interesting to hear from someone with your name, SpeedyMcNameChange!
For the right adult, it's a pretty awesome name :) But I think it would be difficult as a child - especially now with the Harry Potter connection, which I'm sure will still be strong in a few years when OP's daughter is at school.
OP, if you weren't aware of the HP connection, then you should think carefully about it. In the HP books, Luna Lovegood is a very eccentric character, who is called Loony Lovegood by her classmates, and is bullied for being different ( name calling, exclusion, and having her possessions hidden). The name Loony is used a lot, and associations with being crazy pretty much define Luna in the book. She eventually becomes part of Harry's 'outer circle' of friends, and proves a very staunch and capable friend.
The message in the book is that you should look beyond whether someone is popular or not, and whether they're a bit unusual, since what matters is whether someone is a good person and a good friend. She's great from an adult reader's point of view (adults see difference - and being yourself - as a good thing), but probably not so much from a child's view (children tend to be more conformist than adults, and less accepting of difference). I doubt the children reading HP identify with Luna, or want to be her.