Bootstrap News: Image Modifciation

You would have to add the category via PHP on top of the image.

First find the PHP template(s) where your page is rendered. This could be archive.php for the overview. For single posts this is usually single.php, or content-single-post.php. It depends on your theme.

Then you find where the post thumbnail is being rendered, and you add some HTML markup, with the right CSS styles, so that you can place text on top of the image. And then you add the php code for printing the category. For instance:

HTML:

<div class="post-thumbnail">
  <?php the_post_thumbnail(); ?>
  <span class="image-overlay"><?php the_category(); ?></span>
</div>

CSS:

.post-thumbnail {
  position: relative;
}

.image-overlay {
  position absolute;
  top: 10px
  right: 10px;
}

The WordPress Codex is a great place to start learning how to theme in WordPress.