Go to the Australian Website and following instructions Apply for Australian Business Number (ABN)
or go to the Australian Business Registration website (click on following link) http://www.abr.gov.au/ABR_BC/ and go to Apply for Australian Business Number (ABN).
You are only required to register a business name if you want to operate your business in any other name but your own.
So....say I started a lawnmowing business and my name is Joe Bloggs. I am not required to register a business name if I am trading as 'Joe Bloggs'. If I decide to trade as 'Joe Bloggs Lawnmowing', I am then required to register that business name.
To find the application forms go to: