Registration does not give you exclusive rights/ownership of the name. An Identical business name can still be registered by other people in each of the other states.
Do not rely upon business registration or company registration to protect you......Trademark registration will! Trademark registration, if possible, will give you exclusive rights.
Prior to applying for a Business name or Company name, it is highly recommended that you ensure as much as possible, that your proposed name is not going to infringe upon any other organisation's Trademark rights, by having some form of 'search' conducted.
We can assist you in obtaining exclusive rights in use of that name Australian wide!
The more similar your name or brand is to another.......'the more fingers you cross', because you can be sued!
eg: Google , Groggle & Scoogle - The Age - 13/11/10
TradeMarks Australia™ can register Business names in your state on your behalf.