You will need to register a Business Name in Australia unless you are happy to trade under your own name, or fall within an exemption. It is not mandatory for a business to register a Business Name in addition to the default name given to them upon registration.
This depends on your individual circumstances and preferences.
A Sole Trader or Partnership who uses his/her own name or a partnership business who uses the names of all the partners need not register a business name. For example, Josie Smith running her own florist store under her own name need not register a Business Name. However, if she wants to pick the name "Josie’s Flowers" for instance, she will need to register a business name.
A Company trading under its company name “Josie’s Flowers Pty Ltd” for example does not need to register a Business Name. However, if the company wishes to trade under any other name or simply drop the suffix "Pty Ltd" must additionally register a separate business name.