Firstly, congratulations! Secondly, our one twin chose her name really early on but twin B was nameless until she was 4 days old. Then suddenly she was Alyce and It wasn't even a name we had had on our list or even mentioned!
We like a few names like Luna, Amelia, Lyra, Kora, Atari, Askari, Eira, Agatha and of course, our other twin's name - Astryd :)
I like Lyra and Astrid. I'll add them to our list :)