Around line 100 you'll see that the message starts with the store name:
Code:
//send emails
$message = STORE_NAME . " " . EMAIL_TEXT_ORDER_NUMBER . ' ' . $oID . "\n\n" .
EMAIL_TEXT_INVOICE_URL . ' ' .
It doesn't even mention a salutation though.
Perhaps removing the STORE_NAME part from (only) that line may satisfy your needs.
I've only briefly looked at the code, but it seems that while it starts with the store name, it immediately follows it with the order number, etc ... so ... perhaps having the store name, associated with the order number, does make sense after all ...
Anyway, hope that helps you ...