Regardless if you publish a game from your own develop section, or from group creations to anywhere; a group or your profile/your own personal games. It will change the name of the original game, it didn’t seem to disable the game or change anything like the platforms that can play the game. There might have been more that gets changed but this is what I found out so far.
If you have made changes to the game that aren’t the same as the current game, and when you publish it appears to work as intended. Those changes only save to the new created game, and I haven’t test if it still bugs if you publish to an already existing game.