When Merging to PDF from Mail Merge is there a way of saving each doc as address line or similar?

It can be done if the Mail Merge is performed using a script, like this (paid-for) tool I've developed that allows you to do just that (and much more, such as automatically email the merged files to recipients):

https://www.try67.com/tool/acrobat-mail-merge-and-email-pdf-files

I completely understand the challenge you're facing. Unfortunately, when merging to PDF from Mail Merge, Adobe typically assigns generic names to the resulting files (like "PDFMail Merge 1501").Unfortunately, Adobe doesn’t have built-in batch renaming for PDFs from mail merge.