Difficult to explain as different routers do different things.
If a router serves both purposes of handing out IP details to clients via DHCP
and can resolve hostnames to IP addresses via DNS records,
they will create a new DNS record everytime a new client registers for a new IP address via DHCP.
Whenever a client asks a DHCP server for a new IP address (and other details like GW etc), the clients also advertise their own hostname so the router can create DNS records accordingly.
These are sometimes called "smart routers".
But as your hornpidns IP address is probably setup statically, eg. the IP address was not acquired via DHCP from the router, no DNS records are/where created on the router.
Some routers allow you to create DNS records manually.
So you would need to create an DNS "A-record" pointing to the IP address of your hornpidns box.
And if your network is setup for IPv6, you would also need to create an "AAA-record".