Is possible to modify user_login after registration?

WordPress does not allow updating user_login for existing users. You may update it using $wpdb->update as below:

// Sanitizes the username
$user_login = sanitize_user( trim( $user_login ), true );

// Check if the given username exists
if ( ! empty( $user_login ) && ! username_exists( $user_login ) ) {
    global $wpdb;
    //Update user record
    $wpdb->update( $wpdb->users, array('user_login' => $user_login), array('ID' => $user_id));

    // Delete cached user objects
    wp_cache_delete( $user_id, 'users' );
    wp_cache_delete( $user_login, 'userlogins' );
}