Obvious USG answer: The same thing as happens if you have a living terrorist's name. The no-fly list includes dead terrorists in case terrorist identity thieves impersonate them; the Treasury OFAC SDN list (more relevant here, though I do not see David Jones on it) includes dead people because their money does not automatically disappear from their bank accounts and their Amazon Free Super Saver Shipping packages do not immediately disappear from the shipping company's horse-drawn wagons.
What happens when you change your name to a dead terrorists name?
Is there no in government somewhat curious about all the holes in their watch list implementation..