Tom is right… it isn't a copyright issue. But this is a really interesting topic that I have seen pop up here several times. I have a lot of experience with this. I have gone over this with my lawyer for several companies, several software packages, apps, etc…
Copyright and Trademarks are different than patents…
Copyright and Trademarks refer to the name that you are doing business under. The goal of a copyright and trademark s to protect a business from other using similar names that could confuse consumers. I cant open a burger joint named MacDonald because consumers would confuse my business with McDonalds. I could open up a gaming studio named McDonalds because it is not in the same marketplace as hamburgers and you can argue that even though it is the same name, a consumer would be foolish to think a hamburger restaurant and a gaming studio are the same entity. Above, you can see that Bob is creating games under the name of “Sloperama Productions”. That is a brilliant name because it is 100% original. There is nothing out there with a similar name that could ever be considered even close.
I personally always secure a name to do business under and I don't use a personal name (others in the world have the same name). The simplest way to do this is come up with a name, do your web research and if it is available… send yourself a letter describing your intended use under this name is. The Post Office will stamp it with a date… when you get it in the mail, put it in a safe place and don't open it. You can use that as first-in-use. That means is someone comes along 5 years from now and wants to use that name… you have proof that you thought of it first.
The better way to do it is have a lawyer do a search. I have done this for several businesses and it gets pricey. But they can search all of North America under every trademark and copyright to see if there are any similarities that may cause confusion down the road. Then they submit your name to the official US Trademark office.
Tom probably doesn't have a registered Trademark. But he probably does not need it. He has used the name enough in these forums and online to establish himself and the business entity.
Patents
This one is fun. This is where people get screwed in gaming, software, and with technology. A Patent usually refers to a process. Let's say that the game show you are developing the game after had a unique process to play the game or interact with contestants. This process could be outlined into Steps or a structure. If you follow these same steps or structure, that can be infringement on their patent. They may not have a patent. As an example, Google submits thousands of patents to the patent office. Everything from potential tweaks to search algorithms to ideas for gaming platforms (look up patents for Stadia). All of these are available for anyone to read online. To me this is crazy… I love reading patents. Patents tell me which direction specific companies are pushing towards, what their designers are working on and what the future of the marketplace could look like… the patent office is a gold-mine!
You have an idea for the structure of the game you want to create... how it will flow, how users interact… this is where patents are huge. Go to the patent office online and look up anything you can find to see if there is a patent from that show. If not, make sure you copyright your game name as something that could not be confused with the game-show or that consumers could confuse as being associated with the copyrighted game show.
Good Luck!