It is particularly noticeable at Wollman Rink, near the park’s southern edge. Mr. Trump’s name had long been splashed all over the site, which he has run since taking it on as a rescue mission in the 1980s: in big red letters on the dasher boards’ inner walls; on signs listing rules for skaters posted outside; and in big letters near the cashier and skate rental.

But on Tuesday, the name’s presence was greatly diminished. It was gone entirely from the boards, replaced by logos saying “Wollman Rink NYC Central Park.” It was buried in small type at the bottom of a sign listing the rink’s hours and fees. And it was represented by a lone “T” over the skate rental counter.

A representative of the Trump Organization did not immediately respond to a request for comment on Tuesday night. Executives have said in the past that public opinion of the president had not affected the company’s business.

“There is no connection to politics and usership at our facilities here in N.Y.C,” Ronald C. Lieberman, an executive vice president at the Trump Organization, told The New York Times last year.

The changes at the rinks, first reported by The Washington Post, were not sought or required by City Hall, officials said. The Trump Organization, which runs Wollman and Lasker Rink, at the park’s north end, under a contract with the city, informed parks officials over the summer that it planned to alter the signage, without providing details or a rationale.