admin page passing $_POST variables to itself

WordPress passes the page as GET but your form uses POST. The two are different things. POST data never shows up in the URL like this: /wp-admin/admin.php?page=martial-patientenbeheer.php?naam=naam&vnaam= It is sent in the headers.

Put var_dump($_POST) at the top of your callback and you should see your post data. You are looking for the data in the wrong place.