Finding wordpress file in theme editor using the theme name

I’m not entirely certain I understand what you mean but whenever a Page Template is set WordPress also sets postmeta with a specific key and value. The key is called _wp_page_template and the value holds the template location relative to the theme. So you could do this:

$pages_with_templates = new WP_Query( array(
    'post_type'         => 'page',
    'posts_per_page'    => 20,
    'meta_key'          => '_wp_page_template',
) );

This will return a list of pages that have templates, you could narrow it down even more by supplying a value:

$pages_with_this_template = new WP_Query( array(
    'post_type'         => 'page',
    'posts_per_page'    => 20,
    'meta_key'          => '_wp_page_template',
    'meta_value'        => 'template-fullwidth.php',
) );

Now, when I said relative to the theme I mean that if you are using a sub-directory such as:
theme-name/page-templates/template-fullwidth.php the postmeta value will hold:
pages-templates/template-fullwidth.php.

There’s also a conditional to test if the current page is using a specific template:

if( is_page_template( 'template-fullwidth.php' ) ) { ... }

Finally, if you’re using the body_class() function – WordPress will assign a specific class based on the template to the body tag which you could target if you feel so inclined.