If you're okay with everyone assuming that your bub is named after the song (is/was it originally a Catholic hymn?), I think Ave is a pretty name and middle names aren't used too often in every day life anyway.
I've gotta say though, I think I'd feel a bit wrong yelling AVE MARIA YOU COME HERE THIS MINUTE.
Ave Maria has amused me a bit! I probably wouldn't pick it myself. But if you like it, go with it. I was nearly named Michelle after a Beatles song, which is a bit dating. It's my middle name, with a "fashionable" name that dates even worse!
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