Is the company name I want to use available?
A company name is available unless it is identical to a name that is currently reserved or registered under the Corporations Act 2001 for another body, or is identical to a name that is included on the national business names register in respect of another individual or body who is not the person applying to have the name, or is unacceptable for registration under the Regulations.
You can check the availability of a company name on ASIC's name availability check - enter the company name you would like to register and hit the search button. Names that are shown as identical are unavailable, however if it only shows as similar it will usually be accepted.
If the name is available, enter this as your proposed name in the online application (where you can also check availability). There's also the option to provide an alternate name in the event the first preference isn't accepted by ASIC.
Note: This process only lets you know if the name is available on ASIC's registers. It does not guarantee that the name is legally "safe". For example, the name "Nike Shoes Pty Ltd" might be available, but Nike might have a problem with you running a business through this company.