To unmerge customers which invoice under different names and you have merged, use the 'Merge/Rename Customers' button on the Customers tab, which is found within the three dots icon at the top right of the page. 

Select 'Merge/Rename Customers', then find the customer you wish to unmerge and select the trash can symbol to unmerge it, as per screenshots below. 

If you wish to split a customer which invoices under one name into two separate customers rather than one you have manually merged together, see How can I split a customer, for example to track end customers under a reseller agreement?