$categoryID = $product->getCategoryCollection()->getFirstItem()->getId();

$categoryName = $product->getCategoryCollection()->getFirstItem()->getName();

$product->getCategoryCollection()
    ->addAttributeToSelect('name')
    ->getFirstItem()
    ->getName();

$categoryID = $product->getCategoryCollection()->getFirstItem()->getId();
$category = Mage::getModel('catalog/category')->load($categoryID);
$categoryName = $category->getName();

$categoryName = $product->getCategoryCollection()->addAttributeToSelect('name')->getFirstItem()->getName();

/**
 * @param $product_id
 * @return array
 */
public function mc_getCategoryIds($product_id)
{
//       +++ get product the category id
    $registry = $this->mc_C['product'];
    $getObj = $this->mc_get_obj($registry);
    /**
     * @var MagentoCatalogModelProduct $getObj
     * MagentoCatalogModelProduct
     */
    $product = $getObj->load($product_id);

    /**
     * @var MagentoCatalogModelProduct $product
     * MagentoCatalogModelProduct
     */

    return $product->getCategoryIds();
}

/**
 * @param $product_id
 * @return mixed
 */
public function mc_getCategoryName($product_id)
{
    $cats = $this->mc_getCategoryIds($product_id);
    if(count($cats) ){
        $firstCategoryId = $cats[(count($cats)-1)];
        $registry = $this->mc_C['category'];
        $getObj = $this->mc_get_obj($registry);

        /**
         * @var MagentoCatalogModelCategoryFactory $getObj
         */
        $_category = $getObj->create();
        /**
         * @var MagentoCatalogModelCategoryFactory $_category
         */
        $data = $_category->load($firstCategoryId);
        /**
         * @var MagentoCatalogModelCategoryFactory $data
         */
        return $data->getName();
    }
    return 0;
}