When importing shipping and/or billing addresses with your order Shopify requires you to provide the name field OR the last_name field. You do not need to provide both of them, one is good enough. If you are importing a last_name with your shipping or billing address, it would be good for you to also provide a first_name but it's not required.

As you can see above, the fields are marked with at *. Remember you only have to select one of them, NOT both.

When adding the shipping/billing address with your order Shopify will associate them with the customer, if you have provided a customer email with the import.