When you have a CGI program returning a file that is not inline you can control the filename by passing -attachment => $filename into the header method call. I have never included one inline in a web page, but it is worth trying.

If that doesn't work, another solution is to change the URL to include a path after your script. That is instead of accessing a url of the form: http://yoursite/some/path/to/script.pl you'd have them access one of the form http://yoursite/some/path/to/script.pl/somefile.pdf. That will still call your CGI script, but now the client will think the filename is somefile.pdf.