For EU businesses, while validating the EU VAT ID, the business' name is automatically fetched from the EU VAT ID validation service.
If this fails for some reason, or you're not a EU based business, you can generate an invoice containing your Company information after completing your purchase:
In the top-right corner of my website, navigate to the Your Orders page.
Then click "View Invoice" next to the corresponding order. The invoice will open up in a new window.
Click the Update button next to your address information. On the next screen you'll be able to edit the information shown on the invoice to your requirements.