If you are running subsonic on Port 80, then you can easily have a custom domain name... Just go add the appropriate records to the DNS servers hosting your domain, and it will work fine.
For example, if you own "example.com" and want "subsonic.example.com" to point to your subsonic server, then add an A record to your DNS with the address of your subsonic server and the name "subsonic".
If you are not serving subsonic on port 80, it is a little more difficult. You have to know how to set up a web server that will answer back with a "302" message when prompted that redirects to your real subsonic address and port. Continuing the above example, if you want "subsonic.example.com" to redirect to your real subsonic server at 65.66.67.68:4040, then you would have to have the A record above point to a web server you have control of, and would have to set that web server up to answer to the Host Header "subsonic.example.com" and feed back a 302 redirect to
http://65.66.67.68:4040/login.view.
I can help you with specifics in Windows using IIS or apache if you want help setting it up. But your ISP needs to allow inbound port 80 traffic for it to work correctly.
HTH,
Glenn