Trying to sell anyone anything these days is pretty much the-kiss-of-death. People are too distracted by and resentful of advertising.
However, just getting a name (a product name probably) in the public eye without a sales message is valuable. The goal of this is what they call "product recognition".
If in your game world, there were a place for a billboard or a car bumper, you could place a simple message there, just the name of a politician running for office or just the name of a product. You don't want something attention grabbing. You would want something barely noticeable. You want the name in the background not in the foreground. In the case of a politician, you could customize the name to the user's location. Perhaps there is some other place within your game where you could place a name.
The problem all side projects face is "marketing". The product is usually much easier to come by than a way to reach you customers. In your case the problem would be doubled because you need to both market to game players and market the ads to someone.
Good luck!