Need to remove primary doman name in Header above image

Add the following to your style.css

#site-title {
	display: none;
}

You can access style.css by loggin into dashboard and go to Appearance > Editor.

2 ways to remove it.

1. As above, by editing your style.css file found in /wp-content/themes/twentyten/

2. Edit the header.php file in the same directory. It should say this:
<a href="<?php echo home_url( '/' ); ?>" title="<?php echo esc_attr( get_bloginfo( 'name', 'display' ) ); ?>" rel="home"><?php bloginfo( 'name' ); ?></a>

This is line 154 and is the php that echos the blog name to the top of the screen.

Before you go hacking apart a theme, check out Sam Parkinsons great tutorial on building a wordpress theme from scratch.

Cheers
Emile