Another proposal:

use strict;
use warnings;
use feature 'say';

my %tree;
while (<DATA>) {
    chomp;
    my ($id, $pid, $name) = split /,/;
    $tree{$id} = {pid => $pid, name => $name};
}
for my $id (sort keys %tree) {
    my @parent_list;
    my $temp_id = $id;
    while (exists $tree{$temp_id}) {
        push @parent_list, $tree{$temp_id}{name};
        $temp_id = $tree{$temp_id}{pid};
    }
    say join ",", @parent_list;
}

__DATA__
15,10,name3
10,#,name1
12,10,name2
5,12,name4
8,5,name5
[download]

Output:

name1
name2,name1
name3,name1
name4,name2,name1
name5,name4,name2,name1
[download]