That's how I always pronounced the bird (rhyming with clover), but looking it up now, it does actually rhyme with "lover." It's just "lover" with a "p" in front.

(And it's the same for US vs British English, that is, they can both use the rule "p + lover" and pronounce it correctly respectively.)

"Hover" is more ambiguous, though. It can rhyme with "lover" or have a rounder "o" sound.