You can add more input fields inside the default Shopify sign up form as described in this article:

https://shopify.dev/themes/customer-engagement/additional-customer-information


Or, follow these steps:


(1) Open your theme's page:




(2) Click Actions > Edit code




(3) Search for customers/register.liquid file:



(4) Add the following code inside:


<div class="vat">

<label for="vat">VAT ID</label>

<input id="vat" type="text" name="customer[note][vat]" />

</div>



(5) Save your changes



Result: