Sync renamed folders, moved files?

You can try these commerical programs. They can detect renamed/moved files/folders
- GoodSync

File and Folder Move/Rename Detection:
GoodSync detects file/folder renames and executes them as Move commands.

• Syncovery

Detects Moved Files:
If you reorganized your folders by moving files to different locations, Syncovery will detect this and quickly perform the same moves on the other side of the sync, rather than deleting and re-copying the files.

• Bvckup

When a file is moved or renamed at the source, this change should ideally be replicated by simply moving the corresponding files at the destination.

Make sure you test those programs before using them for your real data.