Two Macs, One with settings restored via Time Machine TeamViewer sees the two Macs as the same Mac

I had TeamViewer installed on my Mac, made a time machine backup of that machine, bought a new Mac, and restored the settings to my new Mac.  I then set up my old Mac for my wife to use, with her own software installed.

When I install TeamViewer on the new Mac, TeamViewer thinks that both Macs are the same machine.   I've changed the hostname of the new machine, but TeamViewer still thinks the two Macs are the same machine.  I've  removed and reinstalled TeamViewer on both Macs, but the problem still exists.

What do I need to change on the Mac(s) so that TeamViewer recognizes them as two distinct machines?

Thanks in advance.