Couple of questions before I can help (sorry, but true)
What is your OS (and what release)?
What version of Bridge (and what release) are you using?
What verison of PS (and what release) are you using?
Please go through your process to export the images (screenshots showing which way you are doing the exporting would be helpful as well.
Lastly, when you say "they do not retain the renaming of the file." Which part of the name is not being maintained? The name part of the suffix part? (E.g., "MyPhoto.TIF" is turning into "23425.TIF" or is it "MyPhoto.jpg?"