How to use add_submenu_page() for editors?

You should use edit_posts capability instead of manage_options. manage_options is an administrator level capability. Try the following code –

add_submenu_page( 'woocommerce', 'Name on Menubutton', 'Name on Menubutton', 'edit_posts', 'custom-submenu-page', 'dsrv_init_backend' );