^ Definitely you are right and it should must your license, not on other names.
I suggest to OP to read this article on how to get an online gambling business license, there is no need to rent if you can afford to get your own.
https://meliorgames.com/gambling/online-gambling-license-how-to-get-it/. And I also suggest getting your own lawyer for this and understand first the jurisdiction in your country or in any offshore country that you may choose because they had different rules and laws.
If I were op, I would do what you said and don't have to worry about the cost as when the gambling platform attracts gamblers then the amount of money spent to acquire gambling license and other expenses will be deducted from profit (house edge) as long as the platform survive and stay legit. There is a thread where op is about a gambling site having a domain that is expire and even bought a domain didn't get much attention.