You can operate under a company name as a DBA (Doing Business As), which basically means just you as an individual operating as a company name. The next cheaper alternative would be to self register a corporation (assuming you do some proper homework about corporation types and requirements, taxes, etc.) and get a corporation setup kit for about $300 in most places in the U.S.
There are likely also companies local to you that will help set up new corporations and do corporate filings for you for reasonable prices.
Whether you go DBA and transfer ownership later to a corporation or go straight to registering a corp independently as always it’s preferable to hire professionals for the setup and guidance for good reason.