That's not true. When Robinhood (or any other retail broker) sends orders to a 3rd party to be filled, there is no way for that 3rd party to see who is sending the order other than it's coming from Robinhood. Robinhood maintains their own book customer orders; the FIX protocol that the orders are coded in doesn't even support that kind of granular info.

There are valid criticisms of payment for order flow but privacy isn't one of them.