posts_per_page returning only one post

You may please update your code as follows

   function blog_post_home_shortcode() {
  $query = new WP_Query( array(
        'post_type' => 'post',
        'order' => 'DESC',
        'post_status' => ' publish',
        'posts_per_page' => 3
    ));

  while ($query->have_posts()): $query->the_post();
      $blog = get_the_title();
  echo $blog;
  endwhile;
  wp_reset_postdata();
}
add_shortcode('blogs_home', 'blog_post_home_shortcode');

Please check the above code and let me know if it works for you.