That’s normally not a problem, as long as no one else is already using the name. You can file with the Secretary of State for a protected Trade Name, so that no one else can use the same name in the State of Oklahoma.
There are alot of different types of entities available now, but we normally set up limited liability companies, also called “LLC”.
Every situation’s different, and a corporation may be appropriate. If you have some liability associated with your business, then you may be a good candidate for a corporation.