If a business is VAT registered and a receipt is requested, this appears to confirm the seller’s name and address is required.
"Under UK law, any VAT-registered business must provide their customers with a VAT receipt. That means you’re legally allowed to request one, as are your customers."
"Simplified VAT receipts
VAT receipts with all of the above detail are not always necessary. Retailers can issue less detailed invoices for sales under £250 (including VAT) and are not required to issue an invoice unless the customer requests it. These need only show:
The seller’s name and address
The seller’s VAT registration number
The date of supply (tax point)
A description of the goods or services supplied
If the sale includes items at different VAT rates then for each different VAT rate the simplified VAT receipt must also show:
The total price including VAT The VAT rate applicable to the item
For example, if you buy an electrical item from Tesco for your business (such as a new computer) the price you pay will include VAT at the standard rate (20%). If you also buy postage stamps for your business whilst you’re in the store, these won’t include VAT because they’re exempt from VAT. As the sale includes items at different VAT rates, the VAT receipt must show the different rates"
https://www.accountancyoffice.co.uk/what-is-a-vat-receipt/