Hi there, @Clairedow.
QuickBooks doesn't allow you to enter the same name for a customer and a vendor. You can consider adding a unique character that distinguishes one name from the other.
For example, your supplier's name is Mark and you want to add a new customer with the same name, you can enter a number or a character that identifies the name, like Mark 1. This way, you'll be able to create a new customer.
Once done, you can now create an invoice for your new customer. For more guidance, feel free to watch this video to learn how to create invoices: How to Create a Customer Invoice.
As always, feel free to visit our QuickBooks Community help website if you need tips and related articles in the future.
Please touch base with me here for all of your QuickBooks needs, I'm always happy to help. Have a good day.