With the configuration document above it would imply that I have to have my own domain name registered to set this up?
Yes, you must register a domain.
If you don't want to do this, then you must have a computer on 24/7 to run a dyndns client on the computer behind the TC.
This is from the dyn document.
You must use Dyn Standard DNS with your own domain name for this to work properly. If you intend to use our DynDNS Free or Pro services with an AirPort or Time Capsule, you must use one of our Dyn Update Clients.
A better strategy is just to pay for a static public IP.
Since you have to pay for this anyway.. if the ISP offers a static IP service take it.
Static IP is far more reliable method of connection.