(a) That's right. Under the Business Names Registration Act 2011 (Cth), certain restrictions are placed on business names. For example, a business name will not be registered if it might be confused with another similar registered name; or if it is the same as the name of another Australian company; or if it is offensive or misleading.
It follows that, before attempting to register a business name, a check should be made to ensure the proposed name does not infringe any requirements or limitations that may exist.