Thank you pvonk.
In the side bar of my address book there is a) All Contacts, b) All on my Mac and, c) All iCloud.
When I click on any of them, the listings to the right of the side bar jerk for a second and settle - but not necessarily in the same place in the listings.
And below that, I have a bunch of Smart Groups.
What I am not clear from reading you is what to do next.
Thank you; I looked. Contacts is checked in iCloud on all 3 devices.
And yet, with all 3 devices on my desk, it is still NOT syn'cing that particular name on my Macbook Pro to the other two devices.
Same must be true to names I added to the iMac. What next?
Thank you for your time and advice.