Add this code to your child theme’s functions.php file or via a plugin that allows custom functions to be added, such as the Dessky Snippets plugin. Please don’t add custom code directly to your parent theme’s functions.php file as this will be overwritten completely when you update the theme.

/*
 * goes in theme functions.php or a custom plugin
 *
 * Subject filters: 
 *   woocommerce_email_subject_new_order
 *   woocommerce_email_subject_customer_processing_order
 *   woocommerce_email_subject_customer_completed_order
 *   woocommerce_email_subject_customer_invoice
 *   woocommerce_email_subject_customer_note
 *   woocommerce_email_subject_low_stock
 *   woocommerce_email_subject_no_stock
 *   woocommerce_email_subject_backorder
 *   woocommerce_email_subject_customer_new_account
 *   woocommerce_email_subject_customer_invoice_paid
 **/
add_filter('woocommerce_email_subject_new_order', 'change_admin_email_subject', 1, 2);

function change_admin_email_subject( $subject, $order ) {
	global $woocommerce;

	$blogname = wp_specialchars_decode(get_option('blogname'), ENT_QUOTES);

	$subject = sprintf( '[%s] New Customer Order (# %s) from Name %s %s', $blogname, $order->id, $order->billing_first_name, $order->billing_last_name );

	return $subject;
}