1. If you are logged out you will see “Please log in or Register

else if you are logged in

2. you will see “Welcome USERNAME

<?php  if (is_user_logged_in()) {
          $user = wp_get_current_user();
          echo 'Welcome <strong>'.$user->display_name.'</strong> !';
                        } else { ?>
          Please <strong><?php wp_loginout(); ?></strong>
          or <a href="<?php echo get_option('home'); ?>/wp-login.php?action=register"><strong>Register</strong></a>
          <?php } ?>