Yes, you right, I would never want WP/LR Sync to do it, itself. However, Media File Renamer could do it.
Please contact me directly, and I will try to write you a little script that will hook itself on the WP/LR Sync process, and when an image is re-synchronized, it will call Media File Renamer with the new filename generated by LR.
Normally when Lightroom syncs an image I have it use title,location and date for the filename. The only problem is if I forgot to add a title and location before upload then it was stuck.
I’m a little confused by the media renamer app. I tried it on one file, however in my already created gallery using a gallery shortcode linked to Lightroom, the filename stayed the same viewing the gallery. Also if I click to view the renamed image in the wordpress gallery it would show a completely different image.
I was actually thinking just renaming the file couldn’t work, because it has all the generated thumbnails and even generated webp images unless you rename those too. However I went back into Lightroom and republished the image, then the file renaming seemed to work. I’m actually thinking my safest bet might be to just delete images that have bad filesnames in the media library and republish them in Lightroom unless you have a better suggestion.