Header title

I think you will need to be a little more clear what you mean. Are you talking about in header.php and what shows at the top of your browser window?

Yes, that’s what I’m trying to explain.

do you mean this:
<title><?php bloginfo(‘name’); ?><?php wp_title(); ?></title>

maybe try this:
https://wpcandy.com/articles/tutorials/the-wordpress-help-sheet.html

add the below code inside your functions.php, I assume your theme header.php has do_action(‘wp_head’) action filters.

function my_custom_blog_title(){

	$blogname  = $output = get_option('blogname');
	$separator = ' &#187 '; // raquo >> chars		

	if (is_home()):
		$output .= wp_title($separator,false,'left');

	elseif (is_search()):
		$output  = sprintf(__('%1$s - Search results for: %2$s'),$blogname, wp_specialchars(get_query_var('s'), 1));

	elseif(is_404()):
		$output  .= __(' 404 Error: Page not found');

	else:
		$output = wp_title($separator,false,'right').$blogname;

	endif;

	$output = '<title>'.$output.'</title>'.PHP_EOL;

	echo apply_filters('my_custom_blog_title', $output);
}	

add_action('wp_head','my_custom_blog_title');