How to make a WP_query that returns posts with their category matching a variable page name

I've been looking into creating a wp_query for the wordpress plugin Visual Portfolio that returns posts with categories matching the page name (slug would work aswell) that the widget is on. The goal was to have a single widget on multiple pages that showed different posts. This, atleast to me, seemed like a good way to show different posts on different pages using only that one widget. After looking into it I found my abilities lacking in regard to creating such a query.