For those sites like Jadzia said, you can put anything youd like for the company name, and the reason being is that most companies dont check your name. That would cost them entirely too much money. However, if you would like to create your own company name, its not as hard as you'd think! All you have to do to create a basic company name, this form is known as a DBA (Doing Business As) is to go to your local courthouse to the County Clerk's office. It will cost you about 17 bucks. You'll need your driver's license and the name of your company that you want, and it lasts 10 years (at least in Texas it does but you can find out just by asking). It take a whole 5-10 minutes to setup. Hope this helps!
P.S. There is much more to do when you setup a full blown company, but thats another story, and Ill get into that later. For now this should do you just fine!
*edit: Two questions for you Jadzia, first, would you like to create a company creation post with me? (how to do it, info you need to know ect.), and second (silly one), is that your name or did you pick it off of Deep Space Nine (Im guilty of being trekkie fan :))?