...
open(FILE, "<", $file)
while($z = <FILE>) {
    if ($z =~ <mein pattern>) {
        $key=$1;
        chomp $key;
    }
    if ($z=~ <mein 2. pattern>){
        $value=$1;
        chomp $value;
    }
    $hash{$key}=$value;
}
close(FILE)

open(FILE, "<", $file)
while($z = <FILE>) {
   if ($z =~ <mein pattern>) {
       $key=$1;
       chomp $key;
   }
   if ($z=~ <mein 2. pattern>){
       $value=$1;
       chomp $value;
   }
   push @{$hash{$key}}, $value;
}
close(FILE)

open(FILE, "<", $file)
my $key;
while($z = <FILE>) {
  my $value; 
  if ($z =~ <mein pattern>) {
      $key=$1;
      chomp $key;
  }
  elsif ($z=~ <mein 2. pattern> && $key ne ''){
      $value=$1;
      chomp $value;
  }
  if ($value ne '' && $key ne ''){
      if(exists($hash{$key})){
          push @{$hash{$key}}, $value;
      }
      else {
          $hash{$key}=[$value];
      }
     $key='';
  }    
}
close(FILE);

     if(exists($hash{$key})){
         push @{$hash{$key}}, $value;
     }
     else {
         $hash{$key}=[$value];
     }

[Name11]
text
text
test001
text

[Name12]
text
text
test002
text

[Name13]
text
text
test001
text

...

#!/usr/bin/perl

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

# Datei die überprüft werden soll
my $file = '/path/to/file';
# alle Pattern
my @pattern = qw(test001 test002);
# Hash mit Ergebnissen
my %hash;

{
    open my $fh, '<',$file or die $!;
    local $/ = "\n\n"; # $/ auf "Leerzeile" setzen
    while(my $entry = <$fh>){
        my ($key) = $entry =~ m!\[(.*?)\]!;
        for my $line(split(/\n/,$entry)){
            for my $pat(@pattern){
                if($line =~ /\Q$pat\E/){
                    push @{$hash{$pat}},$key;
                    next;
                }
            }
        }
    }
    close $fh;
}

print Dumper(\%hash);

hash{test001}=[NAME11, NAM13]
hash{test002}=[Name12]

[Name12]
text
text
test002
text