As LanX pointed out, you need to convert the bottom-up "Who is my boss" structure into a top-down "Who are my subordinates" structure, then print the resulting tree.

For example:

use 5.010;
use strict;
use warnings;

# Generalized sample input data (i.e. multiple top-level groups, 
# each with multiple independent bosses)...
my %org_chart = (
    '1929' => {
                '3'    => { 'name' => 'Amy',        'boss' => 1929, },
                '4425' => { 'name' => 'Dwight',     'boss' => 1     },
                '480'  => { 'name' => 'Fry',        'boss' => 2     },
                '1919' => { 'name' => 'Bender',     'boss' => 2,    },
                '1929' => { 'name' => 'Professor',  'boss' => 0     },
                '3968' => { 'name' => 'Cubert',     'boss' => 1929, },
                '1'    => { 'name' => 'Hermes',     'boss' => 1929, },
                '4'    => { 'name' => 'Zoidberg',   'boss' => 1     },
                '2'    => { 'name' => 'Leela',      'boss' => 1     },
    },

    '666' => {
                '666'  => { 'name' => 'Satan',      'boss' => 0     },
                '1'    => { 'name' => 'Beelzebub',  'boss' => 666   },
                '777'  => { 'name' => 'Lucky',      'boss' => 1     },
                '99'   => { 'name' => 'Damien',     'boss' => 666   },
                '333'  => { 'name' => 'Satan Jr',   'boss' => 0     },
                '11'   => { 'name' => 'Unlucky',    'boss' => 333   },
    }
);

# Convert each top-level group into a tree of subordinates...
for my $group (values %org_chart) {
    for my $employee (keys %{$group}) {
        # Who is this employee's boss???
        my $boss = $group->{$employee}{boss};

        # Nothing to do if employee doesn't have a boss...
        next if $boss == 0;

        # Record that this employee is a subordinate of their boss...
        push @{$group->{$boss}{subordinates}}, $group->{$employee};
    }
}

# Draw each group's org-chart (horizontally), 
# starting with boss-less employees...
for my $group (values %org_chart) {
    for my $employee (values %{$group}) {
        # Ignore employees who have a boss...
        next if $employee->{boss};

        # Draw the org chart for employees that don't have a boss...
        draw_chart($employee);
    }

    # Draw gap between groups...
    say "";
}

# Draw each employee and their subordinates tree...
sub draw_chart {
    my ($root_node, $level) = @_;
    $level //= 0;

    # Report the employee...
    say "   |" x $level, "-> ", $root_node->{name};

    # Recursively report their subordinates...
    for my $subordinate (@{$root_node->{subordinates}}) {
        draw_chart($subordinate, $level+1);
    }
}
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