Welcome to the Community family. I have some information about setting up QuickBooks Payments.
When setting up payments, you will require for the Social Security Number. To learn more about this matter, click the link for Why do we ask? in the owner's info section.
With regards to entering the ITIN in the Online Payment set up, I suggest contacting directly to our Merchant Service Support Team. They have the ability to pull up and further check the eligibility of your account for QuickBooks Payments setup.
For future references, you can check the following article about QuickBooks Payments: