/**
 * Implements template_preprocess_paragraph().
 *
 * @param array $variables
 *   An associative array containing:
 *   - elements: An array of elements to display in view mode.
 *   - paragraph: The paragraph object.
 *   - view_mode: View mode; e.g., 'full', 'teaser'...
 */

function MYTHEME_preprocess_paragraph(&$variables) {
  /** @var \Drupal\paragraphs\Entity\Paragraph $paragraph */
  $paragraph = $variables['paragraph'];
  // Get the type
  $parentBundle = $paragraph->bundle();
  if($parentBundle == 'carousel') {
     // Add variables here
     $variables['sitename'] = \Drupal::config('system.site')->get('name');
  }
}

After this, in you paragraph--type--carousel.html.twig you can use:

{{ sitename }}