You are using a very old version of ThumbsPlus, which makes it hard to offer suggestions.
When you look under Options | Preferences | General, is there an option "Allow Folder Operations"? If so, and it is off, then that explains why you could not rename files (turn it on and see if renaming files works).
Other possible reasons why files cannot be renamed include:
• The file is read-only, or it is on a read-only disk (CD-ROM) or write-protected disk.
• A file already exists in the same folder with the same name.
• The file is on a network drive and you do not have sufficient permission to rename it.
• The file is open by another application on your system, or on another system on the network.
• The file doesn't exist (the thumbnail is an orphan).
Generally speaking, when you change the filenames of your images outside of ThumbsPlus (for instance using Explorer or a file manager), then ThumbsPlus can no longer match those files to their thumbnail records in its database. The existing thumbnails for these files, including any keywords and annotations, will become orphaned and you would have to thumbnail the renamed files again (and enter new keywords and annotations).
When you look up one of those renamed files in a gallery, can you still open it in the viewer from there? If so, it would seem that the thumbnail record, and its position in that gallery, are still intact.