Text Formatted Code
<a href="{site_url}" title="{site_name}" itemprop="url">{site_name}</a>
css class site_name or brand_image is set to load an image (class is specified in a previous span I believe.
Remove the {site_name} template variable from between the <a> tags and the name will not be printed. The thing is the H1 tag in the denim theme is set there as well which should have some text in it.
For my themes I have removed the h1 tag from the header and placed it elsewhere.