invoice details split between backend orders and paypal

-- HikaShop version -- : Business 2.6.4
-- Joomla version -- : 3.6.4
-- PHP version -- : 5.6.27
-- Browser(s) name and version -- : Chrome 54.0.2840.87

I am a beginner at this.

When the buyer chooses a product on my site, he clicks on "Choose options".
Then he completes the custom fields and clicks on "Add to cart"
He then sees a "Cart" block (with field details as previously entered) and a "Payment" block. He clicks on "Finish" and is taken to PayPal Standard.

I end up with an entry on my PayPal account showing the transaction number, date, buyer's name, shipping address and email address, the product number and invoice ID.
My backend order shows the HikaShop order number, PayPal transaction number, date, invoice ID, product number and custom field details.

Since PayPal takes the buyer's details, I have not asked the buyer to register or provide these details before being directed to PayPal (I thought I'd keep the transaction as simple as possible).
But as seller, I end up having to take information from both PayPal and the backend Orders before I can fill the order. Also I end up with no record of the customer on my backend.
Am I missing something here?

Thank you Nicolas. They are great options which solve the problem.