When using a USG with Ubiquiti's Unifi Controller software (version 5.6 and earlier), the functionality of integrating the hostnames of clients (when they request a DHCP lease) into local DNS does not appear to work as you would find with Consumer grade routers. To work around this limitation, we can add static host mappings to a configuration file that will be provisioned to the USG when either a configuration change is made or we force provisioning to the USG itself.
I've added in the necessary syntax for adding Cloudflare DDNS to the USG for VPN/Services setup courtesy of this post by britannic on the Ubiquiti Forums.