How do I update every title of a certain category with a phrase

I would use a filter. Sometimes things change and strings have to be translated and so on:

function my_custom_built_title( $title, $post_id ) {
    $post  = get_post( $post_id );
    if ( 'product' == $post->post_type ) {
        $terms = wp_get_post_terms( $post->ID, 'product_cat', [ 'fields' => 'ids' ] );
        if ( in_array( '3439', $terms ) ) {
            $title="Custom build " . $title;
        }
    }

    return $title;
}
add_filter( 'the_title', 'my_custom_built_title', 10, 2 );

I did not test it but it could be a starting point.