First, try to explain in detail what results you are looking for in your first post to the forums. Nothing we like more than having to re-answer a question (over, and over, and over again).
Anyway, this will create a loop of categories, which will then display the posts from each. We’ve changed to category ID numbers because it makes things a little easier here (trust me). Just edit the value of $cat_ids so it represents the categories you want displayed (separate them with commas as below):
<?php
$cat_ids = '1, 2, 3, 4, 5, 6';
$my_cats = explode(',', $cat_ids);
foreach( $my_cats as $my_cat ) :
?>
<ul><li><h2><?php echo get_the_category_by_id($my_cat); ?></h2>
<ul>
<?php
$my_query = new WP_Query('cat=' . $my_cat . '&showposts=-1'); while ($my_query->have_posts()) : $my_query->the_post();
?>
<li><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
<?php endwhile; ?>
</ul>
</li></ul>
<?php endforeach; ?>