The story
Coined by Fur Affinity user TuxedoDragon from amphi- (“opposite”) + -morph (“shape”), ostensibly because the creature can shapeshift between extreme forms. The suffix -o apparently serves to make the name sound more Romance or reminiscent of taxonomic names; this is unetymological, as the origin of Italian, Spanish, Portuguese etc. -o is Latin -us.
Etymology from Wiktionary, CC BY-SA 4.0.