Hi, i'm new to this board, but have some skills by customizing joomla and k2, for displaying the category name in a k2 article, you first have to fetch item attributes, then you can request for category name as follows:
<?php
//get item parameters -> itemCategory
$this->item->params->get('itemCategory');
//display category name
echo $this->item->category->name;
?>
you may not be able to fetch category item if you don't get items specific parameters, most of other item variables are treated the same way
Hope this helped out!.