Unique display name and nickname in wordpress

code.php

<?php

// A dirty script by Ash
add_action( 'personal_options_update', 'check_display_name' );
add_action( 'edit_user_profile_update', 'check_display_name' );

function check_display_name( $user_id ) {
    global $wpdb;
    // Getting user data and user meta data
    $err['display'] = $wpdb->get_var( $wpdb->prepare( "SELECT COUNT(ID) FROM $wpdb->users WHERE display_name = %s AND ID <> %d", $_POST['display_name'], $_POST['user_id'] ) );
    $err['nick'] = $wpdb->get_var( $wpdb->prepare( "SELECT COUNT(ID) FROM $wpdb->users as users, $wpdb->usermeta as meta WHERE users.ID = meta.user_id AND meta.meta_key = 'nickname' AND meta.meta_value = %s AND users.ID <> %d", $_POST['nickname'], $_POST['user_id'] ) );
    foreach( $err as $key => $e ) {
        // If display name or nickname already exists
        if( $e >= 1 ) {
            $err[$key] = $_POST['username'];
            // Adding filter to corresponding error
            add_filter( 'user_profile_update_errors', "check_{$key}_field", 10, 3 );
        }
    }
}

/*
* Filter function for display name error
*/
function check_display_field( $errors, $update, $user ) {
    $errors->add( 'display_name_error', __( 'Sorry, Display Name is already in use. It needs to be unique.' ) );
    return false;
}

/*
* Filter function for nickname error
*/
function check_nick_field( $errors, $update, $user ) {
    $errors->add( 'display_nick_error', __( 'Sorry, Nickname is already in use. It needs to be unique.' ) );
    return false;

}
/*
* Check for duplicate display name and nickname and replace with username
*/
function display_name_and_nickname_duplicate_check() {
    global $wpdb;
    $query = $wpdb->get_results( "select * from $wpdb->users" );
    $query2 = $wpdb->get_results( "SELECT * FROM $wpdb->users as users, $wpdb->usermeta as meta WHERE users.ID = meta.user_id AND meta.meta_key = 'nickname'" );
    $c = count( $query );
    
    for( $i = 0; $i < $c; $i++ ) {
        for( $j = $i+1; $j < $c; $j++ ) {
            if( $query[$i]->display_name == $query[$j]->display_name ){
                wp_update_user(
                    array(
                        'ID' => $query[$i]->ID,
                        'display_name' => $query[$i]->user_login
                    )
                );
            }
            
            if( $query2[$i]->meta_value == $query2[$j]->meta_value ){
                update_user_meta( $query2[$i]->ID, 'nickname', $query2[$i]->user_login, $prev_value );
            }
        }
    }
}

// Call this function once
display_name_and_nickname_duplicate_check();

/*
* Calling the display_name_and_nickname_duplicate_check() again when a new user is registered
*/
add_action( 'user_register', 'check_nickname', 10, 1 );
function check_nickname() {
    display_name_and_nickname_duplicate_check();
}

Paste it in your functions.php file