Register Custom Taxonomy

function register_custom_taxonomy() {
    $labels = array(
        'name'              => _x('Categories', 'taxonomy general name', 'textdomain'),
        'singular_name'     => _x('Category', 'taxonomy singular name', 'textdomain'),
        'search_items'      => __('Search Categories', 'textdomain'),
        'all_items'         => __('All Categories', 'textdomain'),
        'parent_item'       => __('Parent Category', 'textdomain'),
        'parent_item_colon' => __('Parent Category:', 'textdomain'),
        'edit_item'         => __('Edit Category', 'textdomain'),
        'update_item'       => __('Update Category', 'textdomain'),
        'add_new_item'      => __('Add New Category', 'textdomain'),
        'new_item_name'     => __('New Category Name', 'textdomain'),
        'menu_name'         => __('Categories', 'textdomain'),
    );

    $args = array(
        'hierarchical'      => true, // Like categories
        'labels'            => $labels,
        'show_ui'           => true,
        'show_admin_column' => true,
        'query_var'         => true,
        'rewrite'           => array('slug' => 'product-category'),
        'show_in_rest'      => true, // Enable in REST API
    );

    register_taxonomy('product_category', array('product'), $args);
}
add_action('init', 'register_custom_taxonomy');

Usage

// Get terms
$terms = get_terms(array(
    'taxonomy' => 'product_category',
    'hide_empty' => false,
));

// Get post terms
$post_terms = wp_get_post_terms($post_id, 'product_category');