I really don't like
Lucy. It's not technically a bad name, but I find it hopelessly whiny and insufferable. Far too twee for my liking.
It doesn't make sense to me that
Lucy would be a nickname for, say,
Lucinda or
Lucille or whatever, considering they're all elaborations/diminutives of
Lucia, not the other way around. And
Lucia is just the Latinate form of
Lucy, anyway. I think I'd rather see
Lucy NN
Lucilla, not
Lucilla NN
Lucy.
(Actually, now that I think about it, I kind of like
Lucinda, despite its frills.)