You don’t need to register a name but instead as Shawn suggested use a free solution. Of course, make sure your router supports it (asus, no-dns, DynDNS, tzo, zoneddit, etc).
Your router acts as the “server” to monitor IP changes and then updates the domain with the new IP.
Correct once this is setup just change the IP in the app to this domain, ex: wally.no-ip.com
The port forwarding doesn’t change. If it’s working fine then nothing to change.