You can choose whether the system refers to a customer (contact) by Full Name or by File As. In settings, on the first tab (General), about half way down choose the preferred Contacts Display Field:
If you choose File As, whatever contents you put in that field will be used to refer to customers. The system automatically puts Surname, Firstname but you can override this with whatever you want, including an organisation name if you wish.
By default, the display field is Full Name (Firstname Surname).