#!/bin/perl -w
use strict;
use warnings;

my @filenames = ("file1.txt", "file2.txt");

my %result; # Hash of arrays

for my $fname(@filenames){
  my $currentheader = "";
  open my $f, "<", $fname or die "Cannot open '$fname' : $!";
  while (my $line = <$f>){
  	 chomp $line;
  	 next unless length($line); # Skip blank lines
  	 if ($line=~/NAME/){
  	 	$currentheader = $line;
  	 	next;
  	 }
     push @{ $result{$currentheader} }, $line; 
  }
}

# Print results
for my $currentheader(sort keys %result){
	print "\n$currentheader\n";
	print "$_\n" for @{ $result{$currentheader} };
}