This code will display the brand name of each product on the listing.
For the category name, you would need to do something like that instead:
<?php
$db = JFactory::getDBO();
$db->setQuery('SELECT category_name
FROM ' . hikashop_table('category') . ' AS c
LEFT JOIN ' . hikashop_table('product_category') . ' AS pc
ON c.category_id = pc.category_id
WHERE pc.product_id = ' . (int)$this->row->product_id);
$categoryName = $db->loadResult();
echo $categoryName;
?>
To get a link around the category name, you would do instead:
<?php
$db = JFactory::getDBO();
$db->setQuery('SELECT category_name
FROM ' . hikashop_table('category') . ' AS c
LEFT JOIN ' . hikashop_table('product_category') . ' AS pc
ON c.category_id = pc.category_id
WHERE pc.product_id = ' . (int)$this->row->product_id);
$category = $db->loadObject();
$class = hikashop_get('class.category');
$class->addAlias($category);
echo '<a href="'.hikashop_contentLink('category&task=listing&cid='.$category->category_id.'&name='.$category->alias,$category).'">'.($category->category_name).'</a>';
?>