Anakin knew both of the men Rey mentioned. From the network. Not from physically meeting them.
"They don't know I'm here," he said. "Not my Earth identity," he added for clarification. And then he knew he needed to add more, because for some unfathomable reason, everyone else touched by this universe seemed to think the clever use of different names cured bad intentions and deeds. "Not Anakin Skywalker, Darth Vader. Do they?"