If the business doesn't relate at all in industry, you can use the same name.
Like, if you ran a record store and called it 'The Record Store', I couldn't try to register a business with the same name or a variation that's too close, such as 'The Recordstore' or 'Record Store' or 'Recordstore'. If though, I wanted to run a business based on documents as a product and I refered to them as 'records', and I wanted the name to be 'The Record Store', it's okay to do so as long as you're not using a similar or same logo/brand.