Backing Up a Renamed Folder Via Time Machine

Rrenaming makes it a new file to any backup program, as the full path name is the only tag the original and the backup share between one backup and the next. When you rename the file that breaks the association, and the backup utility sees the new name as a new file or folder. Where a full path name is the file name and the names of ALL it parent directories. In the case of Time Machine the starting directory is the beginning of the mounted file system. Different backup utilities will use different starting points.

IF you want an alternate name, consider keeping the original name then create a Mac OS X Alias with the new name or a Unix symbolic Link. These special files are just pointers and backup utilities know they are not the real file, so only the pointer information is copied, not the contents of the file.

Thanks @BobHarris.

I'm no expert, but I wonder if Time Machine could be enhanced to simply make a hard link between the old backup of the file (with the old name) and the new backup of the same file (with the new name). It would really be a nice feature and save a lot of space. In order to implement this, I suppose Time Machine would have to either:

1. keep track of every renaming or moving of a file or folder in some kind of journal or log -- which the HFS+ extended or journaled file system might already be keeping -- and then apply that journal to know when to create hard links instead of new backups; or
2. keep track of the source file's Unix inode of each backed-up file or folder and use that as the key in the Time Machine backup (instead of full path as you said) to look up whether this file was backed up before. During the "import" of a TM backup from an old machine into a new one, it would need to do something like update the inodes in the TM backup to those on the new Mac volume. The import is a great feature; I used it during a recent migration to a new iMac.