integrating some of the suggested functions into your code:
<?php $c_user = wp_get_current_user(); if( !is_user_logged_in( $c_user->ID ) ) : echo '<a href="' . esc_url( wp_login_url() ) . '" alt="' . esc_attr( 'Login', 'textdomain' ) . '">'; echo _e( 'Login', 'textdomain' ); echo '</a>'; wp_register(' / ', ''); else : echo 'Hello ' . $c_user->display_name . ', '; echo '<a href="' . esc_url( wp_logout_url( home_url() ) ) . '" alt="' . esc_attr( 'Logout', 'textdomain' ) . '">'; echo _e( 'Logout', 'textdomain' ); echo '</a>'; endif;?>some remarks:
for the 'Register' link to show, you need to have ticked in the dashboard:'Settings' - 'General' - 'Membership [ ] Anyone can register
the 'Logout' will redirect to the home page; if you don't want that, remove
home_url()from the code