Hi,
That wouldn’t work unfortunately for security reasons, as your players would receive the Forge’s SSL certificate, not your own and I can’t create a certificate with your domain without having access to your DNS (and even if I could, I don’t think I want to be handling user’s SSL certificates at this time).
Also, all of the user’s games are pointing to the same A record anyway (a wildcard CNAME), and the way to know game A vs game B is by checking the hostname, so if you did that, the Forge would actually not recognize the hostname and would not know for which game it’s supposed to be… and will actually redirect you to a google search for “Are you lost?” 
What you can do however is have a webhop, where your domain would redirect your players to your custom Forge URL, so they could still access it from your domain name, but once they do, it would show a different domain in the address bar.
Hope that helps.