You'll need to set a DHCP reservation for each device. The router should then resolve those names for other clients on your network (provided that your hosts use the router for resovling DNS, which they should by default).
To do this, go to the Network Setup page, under the Setup tab on the DIR-567's admin page. Look for the section towards the bottom labelled Add DHCP Reservation.
- The hostname (i.e.
raspberrypi) under Computer Name
- An IP address that falls within the DHCP IP Address Range in the DHCP Server Settings section above
- The MAC address of the device (findable via
ifconfig on Unixes, or
ipconfig /all on Windows)
Check the enable box, then click save. Repeat this for each machine you want to assign a hostname to.