So I proceeded anyhow and hit RESTORE and it seemed to be going in the right direction! It appeared that it was intending to update the software on the device, but it did mention factory settings.
I was given a chance to rename it which I did but then it synced all my content all over again. So I repeated everything and specified not to sync. So I will end up with an iPod with no music on it and not my name. which is what I want.
But, is it connected to my iTunes/Apple account in any way? was it ever? Can it now be connected to anybody's iTunes? Are my iTunes credentials on the device?
As an aside, when renaming the device, I spelled Ipod incorrectly on the device rename, so I went through the restore exercise again. Unexpectedly, the device name field was prepopulated with "My Name's iPod". I'm going to assume that was a cache issue with the software dialog box and My Name was not actually on the device.