How to change the link structure of the homepage?

No need to change core files:

add_action( 'init', 'wpse316713_pagination_base_rewrite_rule' );
function wpse316713_pagination_base_rewrite_rule() {
    global $wp_rewrite;
    $wp_rewrite->pagination_base="image";
}

Go to permalink options page, and press save to flush the rewrite rules, changes should apply afterwards.