I am a truck driver but I have always worked under my name, but now I applied for this company and they are telling me that I have to work under "my name trucking" . Where can I register my new business name?

Depends on where you live, but in general you just use it, no real requirement to register it, if the name requires your own name in the name. You can get a business license under the business name, IF you want to use a name, that does not include you name, you do have to register it with the state. Check with your states attorney general office