Local name resolution works out of the box. Just make sure your use the router as your LAN's DNS. You might also want to define a local domain.
LAN - DHCP Server > DNS Server 1 and 2 should both be empty.
LAN - DHCP Server > Advertise router's IP in addition to user-specified DNS = Yes
Both of these are the default settings, hence it should work out of the box.
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