To do this, please follow the instructions below:

Step 1: In Shopify admin, Go to Settings -> Checkout

Step 2: On Customer information, make Company name Required

Step 3: Back to Settings -> Languages

Step 4: Click on Change theme language

Step 5: Go to Checkout & System tab

Step 6: Scroll down to Checkout contact, find Company label and rename it VAT number (or any type of Tax number you wish to display), then save it

It should look like this on Checkout interface:

Step 7 (optional, only needed if you use Portrait or Landscape template): 

In our app, go to Translations -> Customer, and edit the Company field to be VAT Number (or any type of Tax number you wish to display): 

After everything is finished, here is how the VAT is displayed on the invoice: