I did basically the same you did, and while the files were moved, they weren't renamed.
I copied a whole Album directory to a new directory at F:\AAA, so the path was F:\AAA\The Hard Road\files.flac
I created a new directory at F:\BBB
Using the "Drives & Devices > Explorer" View, I selected all the files in the Album.
Then I used F6, changed the Base Path to F:\BBB, with directory and filename rules so that both would change, selected all flac files, checked the Preview which looked fine, and executed the move.
I tried it with and without directory name changes, testing both or just file name changes. The file name never got changed.
HOWEVER:
I just restarted MC after some time away from it and repeated the test with just one file name change, and it worked.
I used Ctrl+Z to undo the changes in MC.
When I pressed F6 to open RM&CF this time, the Directories checkbox was not ticked, as I had left it that way.
Again I repeated the test with just one file, a new Base Path and directories rule, and a file name change. It worked.
Again, I repeated the test with three files, a new Base Path and directories rule, and a file name change. It worked.
The only other difference from my first tests was that I had turned off the setting "Move all non-imported files in folder with selected media files". So I checked that box again.
I ran the last test again, with three files, a new Base Path and directories rule, and a file name change. This time it failed, with all files in the directory being moved, but none of them renamed. I expected all to be moved and the selected three files to be renamed. It even moved all files when I responded "No" to the confirmation box asking if I wanted to save changes to the three files.
Interestingly, in this last failed test, in the "Drives & Devices > Explorer" View, the three selected files were shown as moved and renamed, while all the additional files were left untouched, in the source directory. However, when I refreshed that view the display was consistent with what I was seeing in Windows Explorer. In previous tests the display in the "Drives & Devices > Explorer" View change as soon as OK was clicked in the RM&CF function, even before I clicked "yes" on the confirmation box. In previous tests when I clicked "No' on the confirmation box no files were moved and the display in the "Drives & Devices > Explorer" View was returned to its original state immediately.
Also interestingly, I couldn't undo the changes with a Ctrl+Z. Ctrl+Z just changed the display in the "Drives & Devices > Explorer" View, but did not move any files back.
So the problem occurs when the "Move all non-imported files in folder with selected media files" setting is checked, and involves update of the "Drives & Devices > Explorer" View, the Undo capability, as well as renaming the files.