A hostname is simply a name assigned to your server for identification purposes. It does not need to be a working domain name and can be anything you choose.
Examples of Hostnames:
myserver.example.com
vps123.softsyshosting.com
customname
Do I Need a Registered Domain for the Hostname?
No, you do not need a registered domain. The hostname is just a label for your VPS and does not impact functionality.