Crazy out of the box thinking. ..but can you name her officially something random but still just call her billie. Ypu know Spocks real name, she very rarely get it, she gets called lou most of the time which is a fair bit different to her real name.

That doesn't help you when picking a name tho =p
This is the same our DS2. He is a Will.iam but we call him L.iam for short. While it's a legit nickname We still get asked if it's one or the other..

Good luck with finding a name! Pity Belinda is out..