I signed up for Dynu Dynamic DNS service. Once it was established, Dynu detected and knew my IP address.
In order to allow updating of the IP address in the future, I followed the instructions on "how to setup the client service for DDNS on Raspberry Pi". But how do I know that it is working? Is there a report on your site that tells me that my client program is sending the information every 5 minutes?

There is an IP Update History section in the control panel that logs all the updates received for a given hostname. But you will have to be a paid member to use that feature. I guess otherwise it would be too much to log for them.

You can also just restart your router and get a fresh new IP and see if the hostname gets updated or not.