Yes, you can add your customer as your vendor. However, you need to add a character or symbol to one of the names so you can save it without any error. You can follow the steps below.
To add a customer:
Click Sales on the left menu and select the Customers tab.
Click New customer on the upper-right corner. Then, type the name, address, and other necessary information and click Save.
To add a vendor:
Click Expenses on the left menu and select the Vendors tab.
Click New vendor on the upper-right corner and type the name, address, and other necessary information. Make sure to add a character or symbol if you're adding the name as our customer.
Once completed, click Save.
Please know that when a customer is also your vendor, these types of transactions between two parties are called Barter Transactions. You may refer to this article to learn more on how to record a barter transaction: Barter transactions.
That should get you pointed in the right direction. For additional information, check out these articles: