choosing a business name

Today in class Mr.Case showed us another business site where it talks about choosing a business name and rules and regulations and how you have to register it.My business is summer time tutoring for grades 1-8 in english and math and bonus reading plus a free snack.The name of my company is now improvement and i have to go to that website and print it put so that its not copied.My budget is about $200.The url is not accesible because i have to ask Mr.Case but i'll get back to you.