Instead of a script, you could set up a table of contents that creates bookmarks for the exported PDF, then split the PDF (in Acrobat, Organize Pages > Split) by top level bookmarks. You can specify how you want the separated PDFs to be named in output options.
If you use data merge to create the letters, just create a field (to merge from the data source, such as recipient’s name or other identifier) just outside the page, touching the edge, or on a separate layer that you can turn off before exporting. Apply a “TOC” paragraph style and then tell the Table of Contents to look for the TOC style. When splitting the PDF, you can use the bookmark names to generate the names for your new PDFs. Hope this helps!