Each post is an object, which changes the syntax you need to use to access the post name:
$arr = get_posts();
$arr = array_reverse($arr);
foreach ($arr as $post) {
echo $post->post_name;
echo "<br/>";
}
As a side point, a slightly easier (and computationally more efficient) way to get your posts in reverse order is to use this instead of array_reverse()
$arr = get_posts(array('order'=>'ASC'));
More fun things you can do with get_posts()’s arguments can be found here and here.