Hi again I think we may be almost there! :-)
Unfortunately I can't modify any DCHP config settings in the router
To be honest, I had been having another "senior moment" and was picturing and old Linux box as the router! I really must learn how to read. :-)
so I have to find a way to either get the Linux PCs to report their host names to the router or have the router find the hostname from the PC.
When booted in Windows they do that but in Linux they do not.
It suddenly occurred to me that this must be the clue. So I went to the man page for dhcpcd (one dhcp client daemon) and found there is both a -H switch, which forces a hostname to that supplied by the server and a -h switch which sends the hostname to the server. I suspect the latter is what windows is already doing. (I mention the former as a reserve in case the -h does not turn out to work.) I also looked at my router (a Linux box) which happens to be using dhclient (another dhcp client daemon) and in its /etc/dhclient.conf there is a place where you can insert send host-name "box1.localdomain" which, it would appear, would do the same thing as above. (I should warn you that I am using SuSE so my /etc/dhclient.conf file may have a lot of stuff in it which is not usually there (SuSE is very good this way; they put it all in and then all you have to do is remove a comment and/or change some text. But the basic behavior of dhclient should be the same.) I'll stop here since I don't know what dhcp client you are using, but I think we are actually knocking on the door!
Of course I can always go back to a static IP and I might just ultimately do that, but I'd like to know if there is a way to make this work.
That is what has got me hooked! doug