I'm having trouble finding the hostname that Dynu wants to see for the Cisco ASA's DDNS interface settings.

Some good news for you, I had two Cisco engineers on the phone and we couldn't get OpenDNS to work and Dynu worked right away. Now, I'm just trying to get the ASA to automate the updates.

Where "hostname" is the name I've used for my domain:
1. hostname.dynu.net
2. hostname.dynu.com
3. api.dynu.com

or, because the ASA software doesn't have username / pw fields, use the url form:
https://api.dynu.com/nic/update?hostname=example.dynu.com&password=PASSWORD

Many thanks in advance!

The hostname should be the hostname.dynu.net where you an replace 'hostname' with the domain you have setup in the control panel.

Thank you very much for your feedback! This information will be useful for those using Cisco ASA.