My understanding is that if a sole trader is VAT registered in 1 business then the 2nd business is automatically VAT registered with the same number even if it's using a different name as it is the person that is registered.
However, if the 2nd business is VAT except, renting spaces in a commercial building, do the invoices for this business need to be VAT invoices?
Any confirmation, clarification will be much appreciated,
Yes if the sole trader is VAt registered then all of his businesses are VAT registered, they fall under his name not under the business name.
Your second point regarding needing to issue VAT invoices the answer again is yes, it doesnt matter that the second business is exempt, its the sole trader that is VAT registered.
Hope this helps