Can't put code to shortcode

Hi all. I want to put this:

<?php
$cat = 2;
$category=get_category($cat);
// echo "<pre>"; print_r($category); echo "</pre>";
echo $category->cat_name;
?>

into shortcode.

For that i doing this:

function cat_name_shortcode( $atts, $content = null ) {
    extract(shortcode_atts(array(
		"name" => '3',
		), $atts));
   return ' <?php
$cat = ' . $name . ';
$category=get_category($cat);
echo $category->cat_name; ?> ' ;
}
add_shortcode('cat-name', 'cat_name_shortcode');

I using this code in template to view shortcode:

<?php echo do_shortcode('[cat-name name="3"]'); ?>

But i getting this on front end:

cat_name; ?>

What im doing wrong and how i can do that?

Thanks.