Allow a full path on the left side of the bar. This would allow renames from wherever they happened to be (potentially quite powerful), and one wouldn't have to worry about finding the original directory again after preparing the set.
You could either allow renaming the paths or not.
But if you did allow renaming the paths, and allowed renaming on the RIGHT side of the bar as well, this would be an extremely powerful, arbitrary move-on-rename feature.
(Sometimes I'll work up a set of renaming pairs in a document using a combination of regular expressions and a little hand editing. When I'm done, I'll not infrequently have to find where the original files were again. If I could simply save the full paths and not just the file/folder name, BRU would in a sense find them for me.)
Also, I think one possible workflow that would be handy is to keep spitting new file sets that need renaming into a text file, then using various editing tools and macros, later just run it through BRU in batches.