Here is a screenshot of the checkout form which shows that First and Last Name is a required field. Although this screenshot does not show it, it forces you to put in a value in the First name and Last name field. I did a test with 'This email address is being protected from spambots. You need JavaScript enabled to view it.' and put in my first name 'Luke' and last name 'Douglas' in the fields.
However, as this screenshot shows, the Name field was not saved (ID=151). You can see that if I registered and then did an order, it does save the first and last name, even dummy ones like 'luketest3 luketest3'. We all know there is no way to authenticate that a valid first and last name was entered so that is not an issue. Not having the name saved at all is an issue.
Here is the Custom fields display which shows that the address_firstname and address_lastname are required fields.
So why isn't the First Name and Last Name saved into the Name field in the customer table?