Using 1.8
There is a function

function blog_name( $format = 'htmlbody' )
	{
		$current_Blog = & $this->get_Blog();
		$current_Blog->shortname( $format );
	}

so you can use this in your _main.php :

<?php $Item->blog_name(); ?>

So I though, lets extend that to

function blog_shortname( $format = 'htmlbody' )
	{
		$current_Blog = & $this->get_Blog();
		$current_Blog->shortname( $format );
	}

so I could use this

<div class="<?php $Item->disp('blog_shortname', 'htmlattr'); ?>">
<?php $Item->blog_shortname(); ?></div>

but that was to simple...

For the divclass determination, I could also use the BlogID, but that is evenly not as simple as I thought...

Yabba, or somebody else.. can you help out please ?

Edit : I found something like this
<?php $Item->get_Blog(); ?>
That is giving me and objectnumber... a strange number, I can not interprete, but at least, for every blog it's giving me another objectnumber...