Here's a way to do it which utilises the power of Perl's arbitrary data structures. Anything you don't understand just ask :)

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

my @AoA = (
    ['tony','skill','old'],
    ['tony','skill','new'],
    ['tony','skill1','old'],
    ['tony','skill1','new'],
    ['martin','skill','old'],
    ['martin','skill','new'],
    ['martin','skill1','old'],
);

my (@names,%hash);

for my $ary (@AoA) {
    my ($name,$stage_name,$type) = @$ary;
    push(@names,$name)
        unless $hash{$name};
    push(@{ $hash{$name}{'stages'} },$stage_name)
        unless $hash{$name}{$stage_name};
    $hash{$name}{$stage_name}{$type}++;
}

# to see the %hash data structure:
print Dumper (\%hash);

print qq|<table style="width:300px">
<tr><th>Name</th><th>Stage</th><th>Old</th><th>New</th></tr>\n|;

for my $name (@names) {
    my $print_name = $name;
    my $stages = $hash{$name}{'stages'};
    for my $stage_name (@$stages) {
        my $stage = $hash{$name}{$stage_name};
        $stage->{'old'} = ($stage->{'old'} ? 'True' : 'False');
        $stage->{'new'} = ($stage->{'new'} ? 'True' : 'False');
        print qq|<tr>
        <td>$print_name</td>
        <td>$stage_name</td>
        <td>$stage->{'old'}</td>
        <td>$stage->{'new'}</td>
        </tr>\n|;
        $print_name = '';
    }
}
print qq|</table>|;
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Output (border added for clarity):

Name	Stage	Old	New
tony	skill	True	True
	skill1	True	True
martin	skill	True	True
	skill1	True	False