You must deal with decoding in your module, but in your script it should work like this:

#!/usr/bin/perl

use strict;

use warnings;

use Encode;

binmode STDOUT, 'utf8';

my $somebody = LdapPerson->new();

$somebody = LdapPerson->search('attila.bardi@example.com');

print "displayname: " . decode('utf-8', $somebody->get_displayName() ) . "\n"

In Dancer you must omit setting binmode on STDOUT, because Dancer sets it itself.  Hope it gives  some hints how to deal with such problem.