You cannot specify region on your module, but you can custom your page or your block.

Regions are specify into main theme.

First, you need to create a folder on your module root directory :

> myModule/templates

Inside, you ll put all your custom template.

For example :

> page1.html.twig

> page2.html.twig

Then you need to declare all your templates :

> In myModule.module :

    /**
     * Implements hook_theme().
     */
    function myModule_theme() {
      return [
        'page1' => [
          'template' => 'test',
          'variables'=>array('test'=>NULL),
          'render element' => 'children',
        ],
    
          'page2' => [
              'template' => 'page2',       
              'render element' => 'form',
          ],
      
      ];
    }

And after, in your controller or your form :

    return $build +  [
      '#theme'=>'page1',
      '#test'=>"its content for my variable inside my template",
    ];