Officials say the new task force number will not be made public.
U.S. military officials in Baghdad tell ABC News that the elite task force dislikes publicity and wants to keep even its task force number secret.
Task Force 145 had already changed its name twice previously, dropping TF 121 and TF 626 as the numbers became more widely known.
The group is made up of elite U.S. military forces, including personnel from the U.S. Navy Seal Team 6, Delta Force and Army Rangers. Members of the British Special Air Service (SAS) are also part of the group.
According to ABC News' Luis Martinez at the Pentagon, the group's first name was Task Force 20, assigned to hunt high value targets in Iraq shortly after the war. They successfully tracked and killed Saddam Hussein's two sons, Uday and Qusay.
They were then merged with the unit looking for Osama bin Laden in Afghanistan, becoming known first as Task Force 5, then Task Force 180.
The players are the same, but the numbers continually change:
Task Force 20Task Force 5Task Force 180Task Force 121Task Force 626Task Force 145Task Force ???