很简单，非常简单。

//firstly, load data for your child category
$child = get_category(31);

//from your child category, grab parent ID
$parent = $child->parent;

//load object for parent category
$parent_name = get_category($parent);

//grab a category name
$parent_name = $parent_name->name;

研究get_category

$thiscat =  get_query_var('cat'); // The id of the current category
$catobject = get_category($thiscat,false); // Get the Category object by the id of current category
$parentcat = $catobject->category_parent; // the id of the parent category

对于WordPress 5.9.
正在获取父类别ID：

$cat = get_queried_object();
$parentCatId = $cat->parent;

正在获取当前类别ID：

$cat = get_queried_object();
$catId = $cat->term_id

按id获取类别名称：

$name = get_the_category_by_ID($catId);

<?php 
    if (is_category()) 
    {
    $thiscat = get_category( get_query_var( 'cat' ) );
    $catid = $thiscat->cat_ID;
    $parent = $thiscat->category_parent;
    if (!empty ($catid) ) {
    $catlist = get_categories(
                                array(
                                'child_of' => $catid,
                                'orderby' => 'id',
                                'order' => 'ASC',
                                'exclude' => $parent,
                                'hide_empty' => '0'
                                ) );

        ?>
            <div class="subcat-list">
                <ul>
                    <?php foreach ($catlist as $category) { ?>
                      <li><a href="<?php echo get_category_link( $category->term_id ); ?>"><?php echo $category->name; ?></a></li>
                      <?php } ?> 
                 </ul>
            </div>
            <?php } } ?>

我知道这是很久以前的问题了，但因为没有一个答案对我有效，所以我决定分享我所做的：

$post_id = 1000;
$category = get_category($post_id);

$category_parent_id = $category[0]->parent;

// It gets the name and not the id or the object
$category_name = get_the_category_by_ID($category_parent_id);

// And here is the parent of the category
$category_parent = get_category_by_path($category_name);