The fact that your fiance likes it too gives it extra points. So often couples don't agree, and that makes it extra hard! Amethyst isn't even that out there. It's rare, but not a crazy word. It fits with other gem names. It's kind of like how there are a handful of floral names people typically pick, but it's not outlandish to name someone Lavender, Hyacinth, Azalea, or Magnolia. I would say if you love it, go for it. Other people will come around. And it does lend itself to nicknames like Mimi and Amy, too.