Go to Appearance >> Header and for “Display Text”, check the button marked “No.”
The text will be gone from the header.
Go to Settings >> General. For “Site Title” and “Tagline” enter the text you want search engines to recognize your site by. Because of the choice you made in the Header pane, this will not show up on your blog, but it will/should show up in most search engines.
Remember, you have no control over what search engines display or how they display it. You can only make it easier for them to find you.