HTML in category name

Thanks all
@ValentinGenev i choose this option, but i’m totally newbie so i Have to study WP much more in order to follow your lead. I found this in my theme (extras.php):

    if ( $child_theme_support == 'default' ) {
        $categories_list = get_the_category_list(esc_html__(', ', 'blossom-fashion-pro'));
    }else{
        $categories_list = get_the_category_list(esc_html__(' ', 'blossom-fashion-pro'));

    }       

    if ($categories_list) {
        echo '<span class="cat-links" itemprop="about">' . $categories_list . '</span>';
    }
}
}
endif;

is the right place to edit with something like this?

$categories = get_the_category();
$category_name="foo1"; // set this to the category name you want to show
$output="";
if($categories){
foreach($categories as $category) 
{
        if ( $category_name == $category->cat_name) 
       {
              $output .='<div class="category-custom-class">'.$category->cat_name.'</div>';
       }
       else
       {
             $output .='<div class="category-custom-class1">'.$category->cat_name.'</div>';
       }
}
echo $output;
}

I’m sorry to bother you with my … inexperience! Thanks in advance