Commonwealth Identity Crime happens where someone takes your personal information and uses it to pose as you, or someone else, to commit, or to help commit, an indictable Commonwealth offence.
The Commonwealth Office of the Australian Information Commissioner has online information to help victims of identity fraud including information about how to apply for a Commonwealth Victims' Certificate. The certificate may help you to negotiate with banks and other financial institutions to re-establish your credentials or to remove fraudulent transactions from records.
The certificate will not automatically re-establish your credit rating, however if fraud is being investigated on your account you can apply to get a freeze on your credit record, and any tainted records can be removed. There is useful information on this on the Office of the Information Commissioner's website: Fraud and Your Credit Report.