The PCN is deemed to be delivered on 20 October which is within 14 days of the parking event, so PoFA 2012 can be used to transfer liability from the unknown driver to you, the known registered keeper. There are other requirements for PoFA 2012 to be valid, but the 14 day limit has been met here.
They can never name the driver in the PCN, all they know is the car’s registration, but they can use that to apply to the DVLA to identify the registered keeper. They often fail the requirements of the legislation to transfer liability, which is why we advise never identifying the driver, but in this case they have complied with the more obvious requirement.
Oh, and it’s not a fine, it’s an invoice for payment under civil contract law based on the driver entering into a contract by parking.