#!/usr/bin/perl -w
use strict;
use Data::Dumper;

my $this = {'data'=>{}, 'name'=>'this'};
my $that = {'name'=>"that", 'value'=>"123"};

$this->{data}->{ $that->{'name'} } = $that;

print Dumper($this);
$that->{'name'} = "them";
print Dumper($this);

This gives me

$VAR1 = {
          'name' => 'this',
          'data' => {
                      'that' => {
                                  'value' => '123',
                                  'name' => 'that'
                                }
                    }
        };
$VAR1 = {
          'name' => 'this',
          'data' => {
                      'that' => {
                       ^^^^       'value' => '123',
                  NOT CHANGED     'name' => 'them'
                                }            ^^^^
                    }                       CHANGED
        };