You have two options...
First, you could use a MySQL database, and when the user uploads the file add the name to the database. Then query the database to retrieve all of the information and make a linked list.
Second, you can upload the file such that the name of the file contains all of the information, and use PHP to read the directory and create a link for each PDF file.
I did the second option for a client that wanted to add PDF's to their website frequently without having to update the site itself. This way you just throw the PDF in a folder, the script reads that directory, converts all underscores to spaces, adds numbers in front of them (or bullets. or nothing) and echo's out a list to where the name links to the document itself.
The PHP.net readdir() info page contains an example script of how to read a directories contents and make a list. You just need to add an if statement so it only displays .pdf files. You'll also want to use the str_replace() function to remove the file extension on your list so it displays:
File 1
File 2
File 3
Instead of:
File 1.pdf
File 2.pdf
File 3.pdf
Hope that makse sense... if you play around with the example script on php.net I'm sure you'll figure it out.