Robin has been in my family as a male name for ages, and I like it enough to use, given enough sons.
I greatly dislike random -y- insertions to make something more 'feminine', so if I were going to use
Robin for a girl, that's the spelling I'd insist on. Especially since, where I live, the Afrikaans word for a ruby is 'robyn', which sounds like rue-BAYn but still makes me pause for a split second when I see it on a human.