Save and user submitted data from a form and display them in the wp backend

Can you just tell me how I can grab the input value for “name” and add the entry to custom_post_type?

Sure thing:

if ( isset( $_POST['name'] ) ) {
    $name = sanitize_text_field( wp_unslash( $_POST['name'] ) );
    if ( $name ) {
        wp_insert_post(
            array(
                'post_title'  => $name,
                'post_type'   => 'my_post_type',
                'post_status' => 'publish', /* Or "draft", if required */
            )       
        );
    }
}