What original name? The only name the airline gets is the fake name that the terrorist provides. The only name the TSA gets is the real name from the ID and the boarding pass. The airline and the TSA don't communicate with each other. All the TSA checks is that you have a boarding pass and an ID. They don't verify that the boarding pass is valid (i.e. that you're an actual passenger on a flight scheduled to depart that day).

EDIT: In case it's not clear, the terrorists prints a fake boarding pass to get past TSA, and keep the "real" boarding pass in their pocket for the airline.