I prefer
Luna in theory.
But I would certainly not have liked to be called
Luna as a child, no matter how pretty it is. For real world use on a human,
Lyra is safer. But it's practically
Lyla, a name I genuinely love.
It's honestly hard for me to picture an actual, everyday person called
Luna. It's just so.... character-y. I know there are lots of Real Lunas out there, but I've not met any. So unfortunately the strongest association I've got is that character
Luna Lovegood. I picture a slightly batty person. Sweet, but not really all there. The eccentricity of it appeals to me. I think of a dog, like a friendly Labrador who is accidentally very destructive. Or a rabbit.
Lyra is also very tied to the fictional character of
Lyra Belacqua or however it's spelled.
Lyra has more dignity than
Luna, but it does feel rather "sneaky" and cunning. It feels like a name for a sleek, elegant nightmare of a person. One of those people who seem polite enough, but they always set you on edge for some reason.