There are several synonyms for the phrase "gotten horn", which refers to the horn on an animal that has grown and hardened. Some synonyms include antler, tusk, spike, prong, and branch. Antlers are commonly associated with deer and elk, while tusks are typically associated with elephants and walruses. Spikes and prongs are often found on various types of animals, including porcupines and antelopes. Branches are a unique type of horn found on certain animals like the moose. While each of these synonyms refers to different types of horns found on different animals, they all share the common characteristic of being used for defense or mating purposes.