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.