How can i add user display name drop down menu in frontend?

Question

How can i add user display name drop down menu in frontend? then user can choose preferred display name?

In fact, I used this code answered here: How to edit a user profile on the front end?

submit handler:

if (!empty($_POST['display_name'])) {
    update_user_meta($current_user->ID, 'display_name', esc_attr($_POST['display_name']));
}

and form:

<p class="form-display-name">
<label for="display-name"><?php _e('display-name', 'profile');?></label>
            <select name="display_name" id="display_name">
        <?php
            $public_display                     = array();
            $public_display['display_nickname'] = $current_user->nickname;
            $public_display['display_username'] = $current_user->user_login;

        if ( ! empty( $current_user->first_name ) ) {
            $public_display['display_firstname'] = $current_user->first_name;
        }

        if ( ! empty( $current_user->last_name ) ) {
            $public_display['display_lastname'] = $current_user->last_name;
        }

        if ( ! empty( $current_user->first_name ) && ! empty( $current_user->last_name ) ) {
            $public_display['display_firstlast'] = $current_user->first_name . ' ' . $current_user->last_name;
            $public_display['display_lastfirst'] = $current_user->last_name . ' ' . $current_user->first_name;
        }

        if ( ! in_array( $current_user->display_name, $public_display ) ) { // Only add this if it isn't duplicated elsewhere
            $public_display = array( 'display_displayname' => $current_user->display_name ) + $public_display;
        }

            $public_display = array_map( 'trim', $public_display );
            $public_display = array_unique( $public_display );

        foreach ( $public_display as $id => $item ) {
            ?>
        <option <?php selected( $current_user->display_name, $item ); ?>><?php echo $item; ?></option>
            <?php
        }
        ?>
        </select>
</p>