You just come up with whatever you want and make sure it's on the Coggins paperwork. Even if you're not showing you can still have a "show name". For those with registered horses, the show name is usually the registered name. However, the show goes by what's on the Coggins and registry papers if both are together, but if you only have a Coggins that is what they go by. For example, on my horse's Coggins is his barn name, even though he is registered, because I don't show and the events I go to don't track points or anything.
Assuming you're in the US of course. No idea what it's like elsewhere!
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