Awesome, thanks for this. I added a line to remove the potentially unwanted “Tag:” bit as well:
add_filter( 'get_the_archive_title', 'remove_category_name_from_archive_title' );
function remove_category_name_from_archive_title( $title ) {
if ( is_tag() ) $title = str_replace( 'Tag:', '', $title );
if ( is_category() ) $title = str_replace( 'Category:', '', $title );
return $title;
}