Sometimes these are called sub domains or vanity domains
Most paid web hosts don’t support this. All the new servers on the system support the wildcard dns needed to run sub domaining scripts. You are free to install your own script/scripts or have your host install one for you to make use of such urls on your web server.
As the upgrades on all our older servers continue, this is one of the many many new features that will be implimented at no cost to most clients that have previously purchased servers.