下記コードを子テーマの functions.php に追記すれば実現できるかと思います。
function customize_page_header_title( $page_header_title ) {
$page_for_posts = lightning_get_page_for_posts();
$page_header_post_type = lightning_get_post_type();
if ( is_single() ) {
$taxonomies = get_the_taxonomies();
if ( $taxonomies ) {
$taxonomy = key( $taxonomies );
$taxo_cates = get_the_terms( get_the_ID(), $taxonomy );
$page_header_title = esc_html( $taxo_cates[0]->name );
} else {
if ( 'post' === $page_header_post_type['slug'] && $page_for_posts['post_top_use'] ) {
$page_header_title = $page_header_post_type['name'];
} else {
$page_header_title = $page_header_post_type['name'];
}
}
}
return $page_header_title;
}
add_filter( 'lightning_pageTitCustom', 'customize_page_header_title' );