Thank you, Dave. Obviously, the Linky is not a DNS server. This would be true whether the clients had static IP addresses assigned or they obtain their IP addresses from the Linky. And yes, there is a search order but that's another story. I was peacefully asleep in my bed.
Guns make less noise.
Since I'm up and bored, I thought I'd check out this DNS thing. It's either this or watch infomercials. I configured the Linky with primary and secondary DNS server addresses. DHCP was enabled for a maximum of 5 clients, starting at address 192.168.1.100. Linky pingable, names resolved.