Thanks for the details. Did some more checking this arvo based on your info and found the following on my Tiger G4.
Queue Name: Canon_LPB@192.168.44.106
Host Name: 192.168.44.106
As you can probably tell, the IP address shown is the Mac Pro sharing the USB printer, and is running 10.5.7. No mention of a host name or any reference to the name shown in the Sharing pane.
By contrast, another 10.5 Mac connecting to the Mac Pro shows the Queue name as the printer@machine_name (no mention of .local) and the host name as "localhost".
So we need to work out where your Tiger Mac is getting the 10.5 hostname of "My-iMac.lan" I believe that your local hosts file is the likely candidate. If not, then it could be the router that connects the two Mac's together.
For a Mac to Mac local network, the Bonjour Computer Name is typically used to identify each Mac on the network. However, if there is a domain name server (DNS) on your network, then this can override the Bonjour name (which is set via the Sharing pane).
What you can do is open Terminal and type the following.
cd /etc "then press ENTER".
This will change your current working directory to the etc directory.
nano hosts "then press ENTER".
This will display the contents of the hosts file and I believe that this may have a reference to the .lan name that is causing the symptom.
If there is no reference to the .lan name then you can exit the nano editor by pressing Control X.
The next thing to try is pinging the name "My-iMac.lan". Open the Network Utility, located in Applications > Utilities, and select the Ping tab. In the address field enter "my-imac.lan" (without the "s) and set the ping count to 4. Now press Ping and see if you get a reply. If there is something associating this name to an IP address, then you should see the IP address in the top line, and if the IP address is currently in use, then you will see replies from that device.
Let me know how all that goes.
PaHu