$rh_dtree = {
             'L1' => {
                       'L2b' => {
                                  'L2b1' => {},
                                  'L2b2' => {}
                                },
                       'L2a' => {
                                  L3b' => {
                                             L4a' => {}
                                          },
                                  L3a' => {}
                                }
                     },
           'L3b' => {
                      'L4a' => {}
                    },
           'L2b' => {
                      'L2b1' => {},
                      'L2b2' => {}
                    },
           'L2a' => {
                      'L3b' => {
                                 'L4a' => {}
                               },
                      'L3a' => {}
                    }
        };
[download]

Main();

Main
{
   my %dtree = init();
   processDtree(\%dtree);
}

sub processDtree
{
   my $rh_dtree = shift;
   
   foreach my $parent ( keys %{$rh_dtree} )
   {
      my @nodenames = ();
      hash_walk( \%{$rh_dtree->{$parent}},[],\@nodenames);
      print join("\n",@nodenames) . "\n";
exit;
   }
}

sub hash_walk
{
    my ($rh_dtree,$ra_keys,$ra_nodenames) = @_;
    
    while (my ($k, $v) = each %$rh_dtree) 
    {
       # keep keys ordered.
       push(@$ra_keys,$k);
       if ( scalar keys %{$v} ) 
       {
          hash_walk($v,$ra_keys,$ra_nodenames);
       }
    }
    push(@$ra_nodenames, join(".",@$ra_keys));
    @$ra_keys = ();
    
}
[download]

The output from running the follows: Note that I am exiting in the first iteration of the foreach loop in processDtree to make it easier to examine the output.

L2b.L2b1
L2b.L2b1.L2b2
L2b.L2b1.L2b2
L2b.L2b1.L2b2.L2a.L3b.L4a
L2b.L2b1.L2b2.L2a.L3b.L4a
L2b.L2b1.L2b2.L2a.L3b.L4a.L3a
L2b.L2b1.L2b2.L2a.L3b.L4a.L3a
[download]

nested-L2b
nested-L2b.nested-L2b1
nested-L2b.nested-L2b2
nested-L2a
nested-L2a.nested-L3b
nested-L2a.nested-L3b.nested-L4a
nested-L2a.nested-L3a
[download]

Copy and paste is your friend. Neither the sample data nor the sample code compile. When the obvious errors are fixed the code only generates the first line of output you show. If the exit is taken out the output still isn't anything like the sample output you give. Even then, the output you show is not consistent with the description you gave in the original node. I notice some duplication in your sample hash - is that intentional?

Show us a self contained script that runs and we may be able to reproduce your results. Anyway, here is my version of something that may relate to what you want:

#!/usr/bin/perl
use strict;
use warnings;

    my %dtree = (
        L1 => {
            L2b => {L2b1 => {}, L2b2 => {}},
            L2a => {L3b => {L4a => {}}, L3a => {}}
            },
        L3b => {L4a  => {}},
        L2b => {L2b1 => {}, L2b2 => {}},
        L2a => {L3b  => {L4a => {}}, L3a => {}}
        );

processDtree(\%dtree);


sub processDtree {
    my ($rh_dtree, @nodes) = @_;

    print join ('.', map {"nested-$_"} @nodes), "\n" if @nodes;
    processDtree ($rh_dtree->{$_}, @nodes, $_) for sort keys %$rh_dtre
+e;
}
[download]

Prints:

nested-L1
nested-L1.nested-L2a
nested-L1.nested-L2a.nested-L3a
nested-L1.nested-L2a.nested-L3b
nested-L1.nested-L2a.nested-L3b.nested-L4a
nested-L1.nested-L2b
nested-L1.nested-L2b.nested-L2b1
nested-L1.nested-L2b.nested-L2b2
nested-L2a
nested-L2a.nested-L3a
nested-L2a.nested-L3b
nested-L2a.nested-L3b.nested-L4a
nested-L2b
nested-L2b.nested-L2b1
nested-L2b.nested-L2b2
nested-L3b
nested-L3b.nested-L4a
[download]

True laziness is hard work