Time Machine dated backups not accessible

MacBook Pro 13,3 – 2016 – Mac OS 10.12.6 (Sierra). I use Time Machine (TM) on an external HD 1TB, directly connected (USB-C). I recently used Migration Assistant to move my whole system from my previous MacBook Pro 8,2 – late 2011, also running Mac OS 10.12.6 (Sierra). I inadvertently used as new name for the system device (now SSD of course) Macintosh HD, whereas the old system device (spinning HD of course) was MyName HD.

When I mounted the TM HD, I responded "Inherit old backups".

After a couple of days I tried to go back in TM history. While the backups prior to the date/time of the Migration still show up as existing, and the dated folders do exist on the TM HD, they are greyed out and inaccessible.

Using Finder, the individual dated backup folders on the TM HD prior to the Migration are called

Backups.backupdb/mynewcomputername/date-time/MyName HD

while those since the Migration are called

Backups.backupdb/mynewcomputername/date-time/Macintosh HD

This likely explains why the prior backups are inaccessible.

So I tried to fix this by renaming my new system device from Macintosh HD to MyName HD. Still didn't help. So I forced a TM backup, and then looked again. Now the dated backup folders:

• prior to Migration are still called MyName HD, and still inaccessible

• since Migration, except for the most recent (forced) backup, still called Macintosh HD, and still accessible

• the most recent (forced) backup now called MyName HD, and is accessible.

So I can still not access the older pre-Migration backups.

I'd appreciate any suggestions using Finder (renaming folders ? – unlikely) or more likely using Terminal commands to InheritBackup or AssociateDisk or other, how to re-attach the backup folders prior to the Migration to the TM accessibility.