Hi Graeme,
As far as I understand, if the customer is not VAT-registered, you do not need to issue a VAT invoice which will have stringent requirements, please see: https://www.gov.uk/vat-record-keeping/vat-invoices
If the transaction is B2C where the customer is not VAT-registered and the customer is paying you at the time the goods/ services are delivered, you can issue a receipt. A receipt as defined by HMRC is a 'which is an acknowledgement of payment.' Similar to receipts you would receive from any supermarket/ retailer, the receipt would only include company information of the supplier and details of the goods sold. In this case, it is not required to add in individual customer names - you can just have a generic customer set up.
However, please do double check this with your accountant!
Tommy