WordPress save the assignment in the post_meta table and so it is easy to get the template name with the default function to return post meta data -
get_post_meta(). The key for the value is
On this point also a small hint: if you will, that you not find your key on the list of post meta keys on the custom fields, create a key with underline and start on the string and WordPress don't list this key in select box; very useful for custom meta boxes on posts and pages.
$template_file = get_post_meta( get_the_ID(), '_wp_page_template', TRUE );