The Trump administration's push to change the Defense Department's name to the Department of War could cost nine figures, according to a new estimate by Congress' budget watchdog.

President Trump signed an executive order last September to start the process of renaming the federal government's largest employer. The agency now refers to itself as the Department of War on its website and in many official communications, though the agency is still formally called the Department of Defense under federal law.

The cost of the renaming effort could range from $10 million to $125 million, depending on how broadly it is applied, the Congressional Budget Office said Wednesday following a request from Democratic Sen. Jeff Merkley of Oregon and Senate Minority Leader Chuck Schumer.

The total price tag could vary depending on how broadly the agency decides to apply the new name and how rapidly the renaming is rolled out, the office said in an 11-page report. 

The lower-end $10 million figure would pay for a "modest implementation" of Mr. Trump's order that just covers the Office of the Secretary of Defense and its departments, according to the CBO. That would cover the cost of replacing "digital templates, office signage, and ceremonial materials" within the office, though the CBO said many of those costs would likely be covered by delaying other budgeted expenses.

The $125 million estimate assumes the name change is applied "aggressively" to both the Office of the Secretary of Defense and "defense-wide agencies" that support the military. Many of those departments — like the Defense Intelligence Agency — have "defense" in their names, the CBO notes, so the cost depends in part on whether their names are also changed. Last year, for example, the Defense Acquisition University was changed to the Warfighting Acquisition University.

Also unclear is whether the department will "rapidly" change its name, requiring it to spend more money to immediately replace signs and stationary, or if it will more gradually roll out the new name "as existing stocks [are] exhausted," the CBO noted.

The CBO said it didn't get information from the Pentagon about the renaming. But a report sent to Congress found $1.9 million in renaming expenses over a 30-day period for five departments within the Office of the Secretary of Defense — which the CBO cautioned could be incomplete. The CBO also looked at the cost of prior renaming efforts, including a decision to rename several Army bases with Confederate names that was reversed by the Trump administration.

The military has not offered its own estimated cost for the renaming bid. CBS News has reached out to the Pentagon for comment.

After Mr. Trump's executive order was signed, a department official told CBS News: "The cost estimate will fluctuate as we carry out President Trump's directive to establish the Department of War's name. We will have a clearer estimate to report at a later time."

At the time, Mr. Trump told reporters the name change wouldn't cost "a lot."

"You know, we know how to rebrand without having to go crazy," the president said. "We don't have to re-carve a mountain or anything...We're going to start changing the stationery as it comes due, and lots of things like that. We're not going to be doing things like have been done in the past, when they change the name of forts that shouldn't have been changed."

By comparison, the military's total annual budget is around $900 billion.

Merkley, the top Democrat on the Senate Budget Committee, called the renaming process wasteful and "performative government at its worst."

"Instead of prioritizing bringing down the cost of groceries or health care, Trump and his cronies are focused on vanity projects like renaming the Department of Defense to the Department of War – potentially costing American taxpayers upwards of $125 million," Merkley said in a statement.

The name Department of War isn't new. From the 1790s to the 1940s, the U.S. military was split into a War Department that oversaw the Army, and a Navy Department that oversaw naval forces and, later, the Marine Corps. After World War II, the two departments were merged into a single entity known as the Department of Defense.

In public remarks in September, Mr. Trump called that postwar renaming "woke." 

"It's gonna fight to win, not to lose. We're gonna go on offense, not just on defense," Defense Secretary Pete Hegseth said, adding that the U.S. will "raise up warriors, not just defenders." 

Chief Pentagon spokesperson Sean Parnell said at the time that the change was a "nod to our proud heritage" and an acknowledgement of the department's "core mission: winning wars."

"This has always been our mission, and while we hope for peace, we will prepare for war," Parnell said. "Defense isn't enough—we've got to be ready to strike and dominate our enemies."