I don't understand how private hosts are associated with public hostnames via the update client.

Imagine I have 3 subdomains sf1.dynu.com,sf2.dynu.com,sf3.dynu.com each of which should point to network and geographically diverse locations. IE: three hosts on three different public networks.

I can best compare by contrast. When I access my router I'm offered several DDNS service provider choices.

They all have three things in common in their setup dialog:

Username
Password
Domain name

That makes sense. The "Update Client" in the router knows it's own IP, so knowing the Username and Password the client crams the IP into the record(s) associated with the Domain Name.

So: I plug sf1.dynu.com into the Domain Name field of router 1 at location 1, sf2.dynu.com into Router 2 at Location 2, and sf3.dynu.com into router 3 at location 3.

But where is the entry for "Domain Name" in the (Linux) config or example config file?

Is the "Domain Name" inferred from the local hostname?

....'cause, I never had to worry about local hostnames before. The local private hostname could be arbitrary as compared to the public subdomain hostname. I mean, do i have to change my private hostnames to FQDN?

What is the REALLY OBVIOUS thing I'm missing?

You can assign different domains to different groups in the control panel at https://www.dynu.com/ControlPanel/DDNSGroup. The IP update client also has a group or location field that you can use to update a particular domain. The association is made by the group.