How is a custom.local assigned to each IP in my local area network?

[psherman]

If you have mdns installed and active on your computers, you'll be able to do host1.local, host2.local, etc..

See this:

DNS update from DHCP

no, this cannot be done (at least not reliably). The .local domain is reserved for mdns. By default, OpenWrt will use the .lan domain, and you can change that to something else, if you so please. That said, if your devices have mdns enabled, you should be able to do this resolution without the router involved anyway. And you can install mdns pacakages on OpenWrt.