I'm curious where would I go to make MyBusinessName Inc.? Legally, Is there some sort of website? And does it cost money? (Dumb Question but I had to ask)
Company registrations are regulated by state governments. I would try to find the portion of your state government website that involves small businesses. Many times a corporation is not needed. Many use an LLC to make life easier. You will have to look into your situation to see what fits. In my state it costs about $130 to register an LLC., more if you want a lawyer to do it. Good luck.
You can go to a site like Bizfilings.com or Mycorporation.com to incorporate online. You could also go to your state's secretary of state's website and find the necessary information there.