Hi Philipp,
When you are in the checkout there is an option to select whether the purchase is being made by an "Individual" or a "Company" - if you select "Company" a field appears where you can enter your VAT number which will then appear on the invoice.
It appears when you made your purchase that you selected "individual". Is this correct?
I will follow up with the accounts department to see if we can get the invoice re-issued for you.
Thanks,
James