Huge Power's Japanese name is Chikaramochi, which translates to Muscleman. But it's also a pun.

Chikara = Power
Mochi = Rice cakes

The rabbit association comes from a Japanese folktale about a rabbit who lives on the moon and makes rice cakes.

Hence why the two fully-evolved Pokemon who get it, Azumarill and Diggersby, are both rabbits. Doesn't explain Mega Mawile, but I guess Mega Mawile's 2 sets of horns could be viewed as similar to rabbit ears.