when we went to incorporate we had to change our name a little bit because our original choice was already taken in our state. As far as any business around here you do need to register it and can't have the same as anyone else.
Our PTO just changed its name from a funky acronym to "PTO". An "old timer" at our school mentioned to me that I need to go down to our county courthouse and verify if the "new name" is in use by any other business before I can claim it as our own and get a new EIN.