Hey there!
At the moment, Shopify’s GraphQL Admin API doesn't support directly setting a customer’s VAT number. What you can do is mark a customer as tax-exempt (which helps with handling tax rules), but the actual VAT number itself isn’t a built-in field you can set through the API just yet.
If you're looking to store the VAT number somewhere, a common workaround is to use a customer note, metafield, or a custom app field to hold that info for internal reference.
Hope that helps clear it up a bit!
