What if you mistype the order number, or forget to provide it? Or when an employee makes a small order that they can just pay immediately with a corporate credit card without first getting approval? Or when a customer pays for something with their personal card and gets reimbursed later by the company? It just makes life a lot easier for everyone involved when the name of the person who made the order is printed on the invoice.

And if people really don't want the supplier to know their name, they just type "IT Procurement" into the name field.