Well, it’s pretty common to handle the naming as you did, where the renamed Sync Clip becomes the region name in the DAW.
If they absolutely positively need the names of the filenames as designated on set, you might achieve that by grabbing all your original audio imports into a new bin, add an audio-only copy of your final sequence, select the sequence and the original audio imports and choose to Relink-To-Selected.
Lots of sound recorders will give certain filenames on set that are not reflected on the clipname in the Avid, since that is usually derived from the metadata in the audio file (that’s the beauty of having metadata rather than just filenams). If they need to destroy this feature, you could try to locate the actual filename (somewhere in one of the bin columns) and copy those entries into the Clip Name column.
All of this will ruin the original (more common and logical) project organization, so I would strongly recommend doing this on a copy of your project, leaving the original project intact.
The true cause of the matter is that ProTools will not read many (if any) metadata that is contained in the Avid and the AAF. Ideally, source filenames, shooting dates, notes, etc should all travel into PT, but this somehow has never been made possible.