I have the following code, but you do not rename the cn, that may be?
$TheDN = "cn=Nombre,ou=Addressbook,dc=axia-ldap,dc=net";
$newRDN = "cn=bill";
$newParent = "ou=Addressbook,dc=axia-ldap,dc=net";
ldap_set_option($ds,LDAP_OPT_PROTOCOL_VERSION,3);
$result = ldap_rename($ds, $TheDN, $newRDN, $newParent, TRUE);