G'day ovedpo15,

I used these steps:

1. Read the file and collect all data in a hash.
2. Generate arrays of ancestry elements for each ID.
3. Sort array elements; join; print.

Here's the code:

#!/usr/bin/env perl

use strict;
use warnings;

my $root = '#';
my %tree;

while (<DATA>) {
    chomp;
    my ($id, $pid, $name) = split /,/;
    $tree{$id} = {name => $name, pid => $pid};
}

my @paths;
push @paths, concat($_, \%tree) for keys %tree;

print join(',', @$_), "\n" for sort {
    @$a <=> @$b || $a->[0] cmp $b->[0]
} @paths;

sub concat {
    my ($id, $tree, $path) = @_;
    $path = [] unless defined $path;
    push @$path, $tree->{$id}{name};

    if ($tree->{$id}{pid} ne $root) {
        concat($tree->{$id}{pid}, $tree, $path);
    }

    return $path;
}

__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]

Note that I changed the last line of your data: s/8,5,name4/8,5,name5/.

Also, it's completely unclear from your expected output, what ordering you wanted in the general case. I've written a sort to give the expected output for a single set of input data. Ask yourself if, given different input, "name2,name1" was "name2,name6,name1", what would the order be? Adjust my "sort { ... }" as required.