Getting Official???

I am wondering at what point I should try to or need to get official.  I have no idea how to go about this.  Is there a difference between an established business name in the city?county?state?-- or like a copyright? I have no idea where to start or what I should do at this very early stage.  I want to protect anything I have from being stolen, yet, I am not earning income or anything so maybe it's just premature.  I wonder if there is an office downtown where I start?  Maybe I just need to google it!!! :)