Most common routers and systems will automatically register and resolve names automatically on the local network. Plus there's zeroconf on top of that. You don't need to manually edit bind zone files for your local network unless you really want to.
I have literally never ever seen a cheap consumer router that did anything "automatically" successfully other than run DHCP and provide access from the LAN to the WAN.
The last two I've used over the last decade have automatically done this. Every machine requesting a DHCP lease is assigned "$host.lan" in the DNS service on the router, where "lan" is a default but configurable domain name.
But even if you don't have this, then zeroconf/avahi/equivalent should be giving you "$host.local".
