Domain names that end in a two letter suffix like .au or .uk are called country code based domain names, also called ccTLDs.

Different countries have different rules for how you can register domain names.

A full list of country codes can be found at IANA

In .au, all domain names must be registered under a second level domain name which distiguishes the type of organisation registering the domain, as per:

.com.au - commercial organisation
.net.au - network provider
.org.au - not for profit
.asn.au - incorporated association
.id.au - individual