As an entertainment lawyer, I'd say lawyers are better than agents. But I'm biased.
Great that you are developing a game show for TV. The first order of business is to finalize the concept and details, the rules, the look, feel and format of the show - honing every detail until it's ready to be shopped around.
What agents and entertainment attorneys typically do is very different. Typically, agents will shop your project around trying to get a studio, production company or producer to buy the show.
Usually entertainment attorneys will be involved in negotiating the deal or drafting the contracts for the deal.
Note that I wrote "typically." While some entertainment attorney's will "shop" material, most do not.
I recommend you get your game show in the best possible shape, then try to get an agent to shop the project around. As interest builds or a deal sounds likely, I suggest then engaging an entertainment attorney.
I wish you the greatest success with the project.
*Disclaimer: This response is for informational purposes only, and is not legal advice. This response does it constitute legal representation, nor does it form or result in an attorney/client relationship.
Maybe that's not the right question, because neither agents for lawyers are likely to want to represent you unless you already have an offer from a producer for your show. and it's a catch 22, because no producer will want to buy your show concept if you're not represented by a reputable player they know and have dealt with, so they know they won't get sued for an idea submission claim, etc.
If you have no contacts of your own, you'll need to develop some, so you can get pitch meetings to sell your concept. And before you do that, you have to make sure that your developed show is registered with the WGA West. Once you've gotten that far, then you can look for a lawyer who will represent you if/when you get offered a deal.
You need a lawyer. For one thing, it's not possible to copyright a stage name, so I think you're worse than a new artist, you're an artist that's confused about what kind of intellectual property you can own and how it's protected. If you are fortunate enough to be offered a recording contract, you definitely need a music lawyer to review it for you, since these are sometimes 80 pp. documents and they can be "360" deals that cover recording, music publishing/songwriting, and merchandizing.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
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