as of WPPizza v3.6.6 – and earlier – you can do this

add_filter('wppizza_filter_email_subject', 'prefix_filter_email_subject', 10 , 2);
function prefix_filter_email_subject($subject, $order){
/* 
$subject is an array made up of 
$subject['prefix'] - typically contains blogname followed by items added to subject line in wppizza->order form 
$subject['main'] - typically contains "your order" localization string (wppizza->localization)
$subject['suffix'] - typically contains date of order according to date/time format set in WP->settings
*/
/* example: adding the "initiator" (i.e payment gateway ident) after the prefix - typically "COD" or "STRIPE" etc, tweak as required, perhaps use some conditionals to change the label to something else if "COD" etc etc */
$subject['prefix'] .= ' '.$order -> initiator;
return $subject;
}

the next / later version will have an additional parameter in the filter that has the order details already formatted

add_filter('wppizza_filter_email_subject', 'prefix_filter_email_subject', 10 , 3);
function prefix_filter_email_subject($subject, $order, $order_formatted){
/* 
$subject is an array made up of 
$subject['prefix'] - typically contains blogname followed by items added to subject line in wppizza->order form 
$subject['main'] - typically contains "your order" localization string (wppizza->localization)
$subject['suffix'] - typically contains date of order according to date/time format set in WP->settings
*/
/* example: adding the label of a gateway as set in wppizza->gateways after the prefix , tweak as required*/	
$subject['prefix'] .= ' '.$order_formatted['ordervars']['payment_type']['value_formatted'];
/* example2: adding the paymet method (i.e typically simply  "Cash" or "Credit Card" ) , tweak as required*/	
$subject['prefix'] .= ' '.$order_formatted['ordervars']['payment_method']['value_formatted'];
/* see $order_formatted for all available parameters */
return $subject;
}

in both cases the $subject array returned will be imploded with a space between each key

NO
you MUST learn about wordpress filters and actions and how they work
https://docs.wp-pizza.com/developers/?section=filters-actions-functions

in fact (and then I promise I’ll shut up 🙂 ) actions/filter hooks exist precisely for the reason that you do not have to touch core files but can extend/change a/some functionality of a plugin/theme/wordpress

apologies, my fault i think (i didnt test this and only did it from memory)

i believe the

$subject['prefix'] .= ' '.$order['initiator'];

in the first example (now corrected) should actually be

$subject['prefix'] .= ' '.$order->initiator;