The rules are that you needed an ABN to get a .com.au and there was a name derivation/check so mycompanyA P/L could buy mycompanyA.com.au but not mycompanyB.com.au. But I've found over the years that the AUDA has relaxed a lot of things and depending on which registrar you go through you can buy pretty much anything you want. It's not enforced anymore. Last time I rang the AUDA (years ago) and asked them what was going on with a customer of mine who had a competitor who got .com.au with
their company name on it, they didn't seem to be able to do anything about it.
So that's the general vibe right now. It's a bit of a mess actually.