Strange! I really like
Griffin, but only because of the mythical beast. If I didn't have that association, I wouldn't like the name at all.
I'm wondering about the "don't name your child after a monster" thing. Maybe it's because when I was a kid, all the books I read that included griffins usually had them as good guys or at least creatures who were on the protagonist's side, so I never really thought of them as monsters.
If you don't want that definition though, my advice would be to go for
Griffith.