Remove author link wherever author’s name is display

You have actually two problems to solve here:

  • The first one is to remove the HTML link, which you are trying to achieve right now. As you read in the comments, it depends on your theme. You could find it looking for the exact HTML displayed around the author name (CSS classes etc), and then seeking for it in the files of the theme (including the WordPress folder perhaps) with an editor.

  • The second issue is less evident but probably more important: you have to actual remove that page. If you just remove the links from your template, the pages will be always visible reaching the URL http://yousite.com/author/username/.

    Getting inspiration by the way SEO Yoast does, you can disable the author archive page with a code like this:

    function disable_author_page() {
        global $wp_query;
    
        // If an author page is requested, redirects to the home page
        if ( $wp_query->is_author ) {
            wp_safe_redirect( get_bloginfo( 'url' ), 301 );
            exit;
        }
    
    }
    add_action( 'wp', 'disable_author_page' );