How do I get simple product name of configurable into checkout Order summary?

You have to write a small extension for that.

1.app/code/Vendor/Namespace/etc/module.xml

  <?xml version="1.0"?>
   <config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Module/etc/module.xsd"> 
     <module name="Vendor_Namespace" setup_version="1.0.0">
     </module>
   </config>

2.app/code/Vendor/Namespace/etc/di.xml

  <?xml version="1.0"?>
    <config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
      <type name="Magento\Checkout\Model\DefaultConfigProvider"> 
        <plugin name="AddAttPlug" type="Vendor\Namespace\Plugin\ConfigProviderPlugin" />
      </type>
    </config>

3. app/code/Vendor/Namespace/Plugin/ConfigProviderPlugin.php

   <?php
       namespace Vendor\Namespace\Plugin;
         class ConfigProviderPlugin extends \Magento\Framework\Model\AbstractModel
           {
             public function afterGetConfig(\Magento\Checkout\Model\DefaultConfigProvider $subject, array $result)
               {
                 $items = $result['totalsData']['items'];
                 $objectManager = \Magento\Framework\App\ObjectManager::getInstance();          

                 for($i=0;$i<count($items);$i++){

                  $quoteId = $items[$i]['item_id'];
                  $quoteNext = ($quoteId + 1);

                  $quote = $objectManager->create('\Magento\Quote\Model\Quote\Item')->load($quoteNext);
                  $simpleProName = $quote->getName();

                  $items[$i]['childname'] = $simpleProName;
                }
                 $result['totalsData']['items'] = $items;
                 return $result;
               }

           } 

4.app/code/Vendor/Namespace/registration.php

      <?php
         \Magento\Framework\Component\ComponentRegistrar::register(
            \Magento\Framework\Component\ComponentRegistrar::MODULE,
              'Vendor_Namespace',
                __DIR__
               );

5.Copy the file (details.html) from below path for your theme.

 vendor/magento/module-checkout/view/frontend/web/template/summary/item/details.html

And then Replace the

 <strong class="product-item-name" data-bind="text: $parent.name">

by

 <strong class="product-item-name" data-bind="text: $parent.childname">

Thanks. Sejal Shah. I refer your extension to do this.