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I would encourage a more descriptive name. The earlier this is done the less work it involves.
Perhaps for easier comparison, here's a query that lists all hexagonal 3-to-6-player variants:
https://www.chessvariants.com/index/mainquery.php?category=Hexagonal&minnumplayers=3&maxnumplayers=6
(There may be some pages listed as primarily 2-player but with 3-player subvariants that this will not find. Dropping the maximum of 6 doesn't include any additional results.)
@Ben Reiniger, I renamed it.
Long ago I overheard a game being proposed where one of the players is not allowed to resign. As someone promptly mentioned, in real life a player could 'resign' by simply getting up and walking away from the game. Nothing can really avoid that, unless somehow said player suffers some sort of penalty, say in a rated tournament situation, or at the least suffers a social stigma of some sort instead.
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It is ready to be published. I didn't find any three-player chess variant that uses the same board, rules and amount of pieces.
Of course, the rules are not final - if you're interested in this variant, you're free to change them at your discretion.