Use the page title in the plugin

You can simply use the get_the_title() function to get the current post’s title in your shortcode. If you want it to work only on pages, you can combine it with is_page():

function shortcode($atts) {

    extract( 
        shortcode_atts(
            array(
                'name' => get_the_title(),
            ) , 
        $atts) 
    );

    // Rest of your code

}

add_shortcode('short_code', 'short_code');

You can use a PHP shorthand conditional as follows:

'name' => ( is_page() ) ? get_the_title() : 'Your else goes here' ;