Shared Disk names not updating
I have found a fix, but I'm not sure what it did to correct the naming issue. While I was researching it I came across the method of connecting to a server by making a bookmark in a browser address bar. In the address bar I typed:
afp://user:password@IPaddressonLAN/iMac%20HD
with the proper username and password for my account on the iMac, the IP address for theIMac, and a %20 in place of the space in the disk's name, iMac HD. Then I selected it and dragged it to the desktop and double-clicking it mounts the desired disk with its new name. And best of all, now if I click on the iMac in the sidebar of a Finder window, it shows the disk as being called iMac HD instead of the old name.
I don't know what this has updated or where, but I'm not complaining if it works! It must have changed something on the iMac, not on my MBA. I say this because I checked with the computer that has never been connected to the iMac - when I posted my question I noted it also showed the old disk name (having never been connected to it at all under that name), and now it shows the new name for the disk. Something has been updated on the iMac itself has to be the explanation.