If you want to show sub category image with sub category name of current category page then follow below process.

Get subcategory of current category

Step 1 : create sub-category.phtml file under ../app/design/frontend/[VendorName]/[theme]/Magento_Catalog/templates/category/

and paste below code inside it

<?php
    $objectManager = MagentoFrameworkAppObjectManager::getInstance();
    $category = $objectManager->get('MagentoFrameworkRegistry')->registry('current_category');    //get current category
    $subcategories = $category->getChildrenCategories();
    $_helper = $this->helper('MagentoCatalogHelperOutput');
?>

<ul class="sub-category">
    <?php
    foreach ($subcategories as $sub_category) {
            $_category = $objectManager->create('MagentoCatalogModelCategory')->load($sub_category->getId());
            $_outputhelper = $this->helper('MagentoCatalogHelperOutput');
            $subcategoryurl = $sub_category->getUrl();            
            $catimgHtml = '';
            echo '<li>';
            if ($catimgUrl = $_category->getImageUrl()) {
                $catimgHtml = '<img src="' . $catimgUrl . '" />';
                $catimgHtml = $_outputhelper->categoryAttribute($_category, $catimgHtml, 'image');
                /* @escapeNotVerified */
                echo '<a href="' . $subcategoryurl . '" title="' . $sub_category->getName() . '">' . $catimgHtml . '</a>';
            }
            echo '<h2><a href="' . $subcategoryurl . '" title="' . $sub_category->getName() . '">' . $sub_category->getName() . '</a></h2>';
            echo '</li>';
    } ?>
</ul>

Step 2 : Add below mention code in ../app/design/frontend/[VendorName]/[theme]/Magento_Catalog/layout/catalog_category_view.xml

<referenceContainer name="columns.top">
    <!-- Add this below code -->
    <container name="category.view.customcatlink" htmlTag="div" htmlClass="custom-category-link" before="category.view.container">
        <block class="MagentoCatalogBlockCategoryView" name="custom.category.links" template="Magento_Catalog::category/custom-cat-links.phtml"/>
    </container>

After that run below commands

– php bin/magento setup:upgrade
– php bin/magento setup:di:compile
– php bin/magento cache:clean

That’s it.

Now, sub category image with sub category name will show on list page.