Assuming that you plan to run an above boards business. That being true, you should consult with an Attorney in your State that specializes in providing documents require to file a business name and all the documents required. That Attorney will also show you where to look for the names of Businesses registered in your State so that you are not using a name already selected or very near the same. As part of all that paper you will receive a Registered Number that will identify your business and also is required for your Business Taxes., local, state and national. As part of the document set development, you will also need to define what type of business you will be, i.e. what Tax structure you select. The Name of Your Business is the easy part!!
Tons more, but at least you know where you really need to start!!
FYI, most States will allow to you use a "DBA" classification as you complete the paperwork! DBA: Doing Business As.
If the group that is or has trained you did not speak about this subject, you should question what else they elected not to cover.
Oh, one more thing: Insurance!!
