“We have a legal name but will be using our colloquial name and the branded acronym 'CFPB,' Ms. Kraninger said in the email, which was provided to The New York Times by a bureau spokesman. “Many of us have legal names but use nicknames without much confusion.”

She added: “I believe this decision is most efficient and effective for our continued work together.”

The consumer bureau was created during the Obama administration under the Dodd-Frank Act and many Republicans have accused it of regulatory overreach. When Mr. Mulvaney took over as acting director from Richard Cordray last year, he put a freeze on much of the agency’s enforcement activity and, to the chagrin of much of its career staff, decided to rebrand it.

“We changed the name because it’s the name in the statute,” Mr. Mulvaney told reporters at the agency’s offices last June. “If your whole theme is going to be to follow the statute, I thought it was a good, small way, but a very visible way, to send a message.”

As part of Mr. Mulvaney’s directive, the letters on the bureau’s offices were reshuffled to read B.C.F.P. and he was in the process of reformatting stationery and other materials to make the change official. According to an internal analysis, which was first reported by The Hill, the costs of these changes to the companies regulated by the bureau could reach $300 million.