Richard here from Shopify! Thanks for your question here. There are actually some folks discussing this over at this forum post here.
The answer at this stage is that Shopify doesn't currently have a slot for VAT numbers to be entered.
One workaround we have at present is to create your own field in the cart as per this guide
I would recommend checking back in on the forum post mentioned there, several merchants are discussing other workarounds to this issue there :)