Not sure I understand. Have you hardcoded those file names in the system call? I would guess that you get the input file names from somewhere (listing directory contents, some config file, user input...). Otherwise, how would the program work if there's a new date stamp...
So why not simply dynamically create the output file name according to the date stamp found in the input file? For example:
my $in1 = "exhibit1_29JUN2010.pdf";
my $in2 = "exhibit2.pdf";
my ($date) = $in1 =~ /_([^_]+)\.pdf$/; # extract date
my $out = "exhibits_$date.pdf"; # create output file name
system "pdftk /home/Memos/$in1 /home/Memos/$in2 cat output /home/Memos
+/$out";
Or maybe
my $dir = "/home/Memos";
my $in1 = <$dir/exhibit1_*.pdf>;
my $in2 = "$dir/exhibit2.pdf";
my ($date) = $in1 =~ /_([^_]+)\.pdf$/;
my $out = "$dir/exhibits_$date.pdf";
system "pdftk", $in1, $in2, "cat", "output", $out;