https://a.pgtb.me/Z7wM28
You can submit the name in the form on this site.
It has the naming rules and links to check the JC registry. It's always exasperating when people just start brainstorming very obvious names you know are taken and they clearly didn't bother to check. Happens every time there's a naming contest.
I'm guessing the very last 'not-eligible' rule, "Names of horses appearing within the first five generations of the pedigree of the foal for which the attempt is made." is to do with things like Arlucea, both the dam of Bayakoa and the name of one of her daughters. I don't know why they ever named a foal that again in the first place but it'd definitely lead to confusion.