Just want to know what inspired the creation of calyrex.
Calyrex may be based on an arctic hare and a crown. The large bulbs on its head and around its neck resemble berries or flowers. It also bears some resemblance to fictional taxidermy creations, such as the American jackalope or the German wolpertinger. Its beads around its neck each bear the Hōjō clan symbol. Conceptually, it may be based on pre-Victorian depictions of fairies and elves, or any one of a number of Horned deities from various European pagan religions, such as Cernunnos or Herne the Hunter. Its fusion forms appear to be a reference to cavalry, or the folklore of the Wild Hunt.
As for its name:
Calyrex may be a combination of calyx (Latin for bud) and rex (Latin for king), or carex. Budrex may be a combination of bud and rex (Latin for king).
Calyrex may be a combination of calyx (Latin for bud) and rex (Latin for king), or carex.
Budrex may be a combination of bud and rex (Latin for king).
Source
Hope I helped!