Pipemonk will sync both customers into QuickBooks Online. Please note that the customer with the duplicate name will have his or her e-mail appended to his display name in QuickBooks Online.
For example, if you have two customers with the Name as ‘Tom Carter’ in Shopify:
The first customer would be synced as “Tom Carter”.
The second customer would be synced as “Tom Carter-tomcarter@abc.com” (assuming tomcarter@abc.com is the email id).
But if the second user doesn't have the email Id, then in that case:
The first customer would be synced as “Tom Carter”.
The second customer would be synced as “Tom Carter-(1). The name will be simple appended by "(1)".