Hello vermar,
You can run the client directly from the server or from your router, AVMs FRITZ!Boxes for example have the option to configure dynDNS directly.
ddclient is available from the repositories and can be installed directly via univention-install ddclient.
However there are more things to keep in mind: If you are not familiar with servers in general I would not recommend to run UCS publicly available as its intended usage is at least behind a firewall. You can check the Cool Solution - UCS reachable from the Internet for more info on what to think of.