.onion addresses work somewhat similar to Bitcoin addresses in that they both use a public/private keypair. In order to host a particular .onion website, you will need the private key for that .onion address. Similar to Bitcoin addresses, it is unlikely that two people will generate the same .onion address based on the private key they create, and owners of .onion websites can use a "vanity generator" to create a "vanity" .onion address.
It is my understanding that the amount of resources it takes to generate a .onion address is similar to the amount of resources it takes to generate a Bitcoin address, however if you change the .onion address of your tor website, then you will need to tell anyone who wants to access your website your new .onion address (which creates security issues).
I understand that part. I was mainly concerning a previous post in this thread that reported the .onion addresses for sites owned by moriarty changed very often:
These onion sites change url monthly. They changed url dozens of times.
However, the onion site URL seems to have kept consistent from September to the time of your report, so I will add them to the OP. Thanks.