That can work, if your LAN router's DHCP and DNS are set up to respect the hostname suggested by the client, to update it in the DNS for the LAN domain, and tell DHCP clients to use the router for DNS.
For LAN devices you want to access as a server, I think it's usually easiest and most reliable to just designate a permanent IPv4 address for them with your router's DHCP server, like what OP suggested.
Your SSH client will probably prefer static IP addresses, too, for the record-keeping it probably does about which servers it knows and at what addresses.
For LAN devices you want to access as a server, I think it's usually easiest and most reliable to just designate a permanent IPv4 address for them with your router's DHCP server, like what OP suggested.
Your SSH client will probably prefer static IP addresses, too, for the record-keeping it probably does about which servers it knows and at what addresses.