It is the law. If you intend to trade under a particular name it must be registered with ASIC. The consequences of trading under an unregistered business name are twofold:
1. It is an offence under section 18 of the Business Names Registration Act (Cth) to carry on a business under an unregistered business name. Failure to adhere to this provision will result in a penalty of 30 penalty units ($3300).
2. Chances are, if you haven't registered the name, someone else may have. In fact, they may even have intellectual property rights in the name by way of trademark or copyright. This opens you up to a civil action governed by the Trade Marks Act 1995 (Cth). If infringed, the trademark holder can enforce his/her proprietary rights in order to seek an injunction (to stop you from using the name), damages (paid by you) or an account of profits (you hand over all money earned under that name).
Aside from the strictly legal and financial ramifications of trading under an unregistered business name, your reputation will almost certainly take a hit.