A domain name is like a business name, you need to register it and assign it to an owner, you don't have to host it anywhere if you just want to register the name to protect it and have ownership of the domain name. The are many extensions available for domain names (.com.au/.net etc)
To enable the domain name to actually do something when entering the address into a web browser or using it as your email address, you need hosting. Packages for hosting vary, depending on your budget and space requirements.
See domain names available at https://databit.au