I dont know whether i understood the OP question correctly or not. I have written a snippet which will change all the "that" in keys/values to "them". Correct me if i am wrong.

Added some more elements in to that hash for navigational purpose.

#!/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;

$this->{data}->{that}->{abc}->{that}="them";
$this->{data}->{abc}->{that}->{that}->{that}->{abc}->{that} = "them";
$this->{data}->{abc}->{that}->{that}->{that} = "abc";
print Dumper $this;
my $struct = &change($this,"that","them");
print Dumper($struct);

sub change {
    my ($struct,$input,$output)=@_;
    if ((ref $struct)=~/HASH/){
        foreach my $t (keys %{$struct}) {
            if (ref $struct->{$t}) {
                if ($t eq $input) {
                    my $k = $struct->{$t};
                    $struct->{$output}=$k;
                    delete $struct->{$t};
                    &change($struct->{$output},$input,$output);    
                }
                &change($struct->{$t},$input,$output);
            }
            else {
                $struct->{$t} = $output if    ($struct->{$t} eq $input
+);
                if ($t eq $input) {
                    my $k = $struct->{$t};
                    $struct->{$output}=$k;
                    delete $struct->{$t};
                }
            }
        }
    }
    return $struct;
}
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