#!/usr/bin/perl

use strict;
use warnings;
use Data::Dumper;

my %hash;
$hash{test001}=['NAME11', 'NAM13'];
$hash{test002}=['Name12'];

my @array = qw(NAME13 NAME14 NAME15);

for my $key(keys %hash){
    if(grep{my $i = $_; defined $i and grep{$_ eq $i}@array}@{$hash{$key}}){
        print Dumper($hash{$key});
    }
}