Using dynamic templates in custom module

I have created a custom Drupal 9 module, and I would like for this module to use different template files basing on a variable. I have looked at hook_theme() and I think the pattern return value might be what I am looking for, but I can't seem to make it work.

testpage.module

function testpage_theme() {
  return array(
    'testpage' => array(
      'template' => 'testpage',
      'variables' => array('items' => array(), 'title' => NULL),
      'pattern' => 'testpage__'
    )
  );
}  

### Controller file (Testpage.php)

```php
namespace Drupal\testpage\Controller;
use Drupal\Core\Controller\ControllerBase;
use Symfony\Component\HttpFoundation\Response;

class Testpage extends ControllerBase {

  public function Render($name) {
    $result = "Lorem ipsum";
    $build = array(
      '#theme' => array('testpage__'.$name, 'testpage'),
      '#items' => $result,
      '#title' => 'Testpage',
      '#cache' => [
        'max-age' => 0
      ]
    );

    return($build);
  }
}

I created three template files in a "templates" folder.

• testpage.html.twig
• testpage--test.html.twig
• testpage--test2.html.twig

Basing on $name, it should use the matching template file. However, it is always just using the markup from the testpage.html.twig. When $name is equal to "test", it should use the testpage--test.html.twig file; when $name is equal to "test2", it should use the testpage--test2.html.twig file. And it would be great if it would use the testpage.html.twig file as a fallback if a matching template does not exist. I thought this was possible with the pattern return value, but I can't seem to get it to work correctly. Am I missing something, or is this not possible?