WASHINGTON — Renaming the Department of Defense the Department of War could cost U.S. taxpayers as much as $125 million depending on how broadly and quickly the change is made, according to an analysis released Wednesday from the Congressional Budget Office.

President Donald Trump signed an executive order in September that authorized the Department of War as a secondary title for the Pentagon. At the time, Trump said the switch was intended to signal to the world that the U.S. was a force to be reckoned with, and he complained that the Department of Defense’s name was “woke.”

Indeed, the order came as the military began its campaign of deadly airstrikes against alleged drug-carrying boats in South America. Since then, a stunning military operation has captured then-Venezuelan President Nicolás Maduro and the Trump administration has threatened military action in places from Iran to Greenland.

Congress has to formally approve a new name for the department, and it has shown no serious interest in doing so. Nevertheless, Defense Secretary Pete Hegseth embraced the rebrand and proceeded to use it immediately on several signs after Trump’s order.

He had employees remove the large gold letters that spelled “Secretary of Defense” outside his office and replaced the sign on his door to read “Secretary of War.” The Pentagon’s website also went from “defense.gov” to “war.gov” the same day the executive order was signed.

Pentagon officials said then that they could not offer a cost estimate for the name change because they expected costs to fluctuate. They promised a clearer estimate later.

The new report from the Congressional Budget Office says costs would be at least a few million dollars if the name change was phased in with minimal implementation, but could reach $125 million if it was implemented broadly and rapidly throughout the department.”

The assessment said it would cost roughly $10 million for a “modest implementation” of the executive order if the name change happened within the agency, and such a cost would most likely be absorbed within the Pentagon’s existing budgets.

“A statutory renaming could cost hundreds of millions of dollars,” depending on how Congress and the Defense Department choose to to do it, the report says.

The Pentagon has more than 6.5 million square feet of office space, and many of the signs, logos and seals have remained unchanged. It is not clear if the push to alter the Defense Department’s name has been carried out at the numerous military facilities across the world.

Republican lawmakers, including Sens. Mike Lee, Rick Scott and Marsha Blackburn, introduced legislation to make the name change official shortly after Trump signed the executive order but the measure has not progressed.

The order had tasked Hegseth with recommending actions required to change the name permanently. Pentagon officials did not answer questions about what, if any, recommendations have been made.

The new analysis was requested by Senate Democratic leader Chuck Schumer, D-N.Y., and Sen. Jeff Merkley, D-Ore.

Lawmakers established the Congressional Budget Office more than 50 years ago to provide impartial analysis to support the budget process.