It can be useful to have the router's internal DNS serve records for hosts on the LAN, especially if those hosts have RFC1918 addresses. Saves messing with /etc/hosts on multiple machines.
Adding host entries
"Network Setting" > "DNS"
Note there's a open bug that in current (Oct 2016) firmwares hostnames can't have dashes/hyphens in them.
Autoconfiguring resolvers on LAN hosts
If LAN hosts autoconfigure their networking using DHCP (IPv4) and RA (IPv6), then one needs to point the hosts at the router's DNS.
Go to "Network Setting" > "Home Networking"
Under "DNS Values", set to "Static" and set "DNS Server 1" to 192.168.1.1 (unless the router has a different IPv4 address).
Under "IPv6 DNS Values", set "IPv6 DNS Server 1" to "User Defined" and enter the IPv6 LAN address of the router. Set the other IPv6 DNS Servers to "None".
Setting search domain
To set the search domain of resolvers, "Maintenance" > "System" and change (at least) the domain name of the router.
Such changes to the router's configuration will be overwritten if one sends a new configuration to the router from the Control Pages.