From what I understand, you just need to use this in your template as it sounds like you will be using an archive page for a given CPT.
<h1><?php post_type_archive_title(); ?></h1>
I've not been able to test this but you can find more info about the options on this Wordpress Codex page.
There are other solutions based on how your page is going to be displayed so feel free to give more info if this doesn't work.
Based on your comment, you may be able to use a simple tag like this...
<h1><?php echo single_cat_title(); ?></h1>
If it still won't play you may need to go slightly more in depth and I'll need to do that from my main computer later as I have done this same thing recently.