Yes, you can add your company name information to a custom invoice after purchase.
​

You can see what a Leanpub PDF invoice looks like here.

Here are the instructions for creating a custom invoice for your purchase, which you will receive in a new email, as a PDF attachment:

http://help.leanpub.com/en/articles/117489-i-am-going-to-need-to-add-company-information-to-my-purchase-receipt-how-can-i-do-that

The PDF is titled Leanpub Invoice, and it is a properly-formatted invoice, not just a receipt.
​
​It has an invoice number, it shows the amount that was owed, the fact that payment has been provided, a $0 amount due, our company information, etc.

In terms of your company VAT, you provide that at checkout by selecting that you are purchasing as a business, and adding your EU or UK VAT number to the form.
​
Here's a screenshot of what this form looks like when you check out with PayPal. Note that we only show the "I'm purchasing as a business" check box on the PayPal form if you have selected an EU country, or the UK:
​

Here's a screenshot of what this form looks like when you click "Check Out with Credit Card" to pay with Stripe. On this form, the "I'm purchasing as a business" checkbox is always shown:
​