How does the name you give your game affect its success?
As the developer, I can give you a definitive answer:
Whether or not you give your game a custom name does not affect the value of the ratings.
However, if you simply leave the name as Game #X, it can cause some tongue-in-cheek responses from the reviewers who will refer to this fact. It doesn't change the value of the review, it just changes the text.
We just thought of it as a friendly poke to say that the game world cares about the name but we didn't want to actually penalize players for not naming their games.