Two of Donald Trump's oldest businesses - a pair of ice rinks in Central Park, which the US preisdent has run since the 1980s - have started removing his name from their branding.

As skating season begins, the president's name is gone from the boards around each rink, where large red “TRUMP” signs once surrounded skaters.

It is mostly gone from the desk where visitors rent skates: There, the white tarpaulin used to hide the his name wasn't quite big enough for the job, so a “T” still sticks out.

Where the president's name remains, it is largely relegated to the fine print. The welcome sign out front of one rink used to say “Trump” at the top; now the name is at the very bottom, under the phone number. “Operated by the Trump Organisation,” the sign says.

Mr Trump's company still runs these two ice rinks. For them, then, the changes in branding mark a milestone: For the first time since Mr Trump took office, two of Mr Trump's own businesses seem to be trying to downplay their connection to his name.

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“It's a complete rebranding,” said Geoffrey Croft, of the watchdog group NYC Park Advocates. These rinks, which once shouted the president's name, now barely mention it. “They've taken [the name] off everything. Off the uniforms, everything.”

Mr Trump has run the rinks since the 1980s, under a concession from the city of New York.

They actually played a major role in the creation of Mr Trump as a national celebrity: in the 1980s, he took over a languishing city-run renovation project and famously finished the rink himself, on time and under budget.

Officially, they have other names: Wollman Rink in the southern part of the park, and Lasker Rink at the park's northern end. But Mr Trump displayed his name as prominently - or more prominently - than the official names.

The two rinks had been heavily branded with the Trump name through last winter's skating season.

This summer, a city spokeswoman said, the Trump Organisation decided to make a change.

“The Trump organisation notified us in late August that they planned to change the on-rink branding,” Crystal Howard, a spokeswoman for the city parks department, said in an email.

She said the city did not ask for the change and that the company did not explain why it did it.

When a reporter from The Washington Post visited Wollman Rink on Tuesday, the only prominent appearance of the Trump name was on the Zamboni ice-resurfacing machine. Employees weren't sure if it would stay there, either. Croft, the parks watchdog, said an employee had told him it would come off.

The Trump Organisation did not respond to questions about the change.

When a Post reporter visited the rink this week, one employee theorised that the decision was made because the Trump branding was driving some customers away.

Mr Trump offered to renovate the rinks in the 1980s and has run them under his brand ever since (AP)

“I do believe that's the answer. It was hurting business,” the employee said. The employee spoke on the condition of anonymity because he was not authorised to speak to the media. “A lot of the schools, you know, liberal private schools up here, come to parties up here. That was a big income earner up here Monday and Tuesday night.”

The New York Post reported on one instance of that in early 2017: a skating party at the Wollman Rink for children from the elite Dalton School was cancelled, the paper reported, after some parents refused to let their children go to a rink emblazoned with Trump's name.

Mr Trump built an empire on branding, leaving his name on dozens of hotels, buildings and golf courses. Since Mr Trump took office, his name has been removed from three hotels and six Manhattan residential buildings. But those were other people's buildings, whose owners had paid to license the Trump name.

The ice rinks, by contrast, are run directly by Mr Trump's company. The change is their decision, the city said. The Post has not identified any other instances in which the Trump Organisation voluntarily removed so much Trump-branded signage from any property.

These ice rinks are - like many other Trump properties - marooned in a liberal city, far from the rural and exurban voters whom Mr Trump relies on as a politician.

In 2015, Mr Trump quickly reversed his public image, from a hotel owner who courted urban elites to a hard-right politician who denounced them.

But unlike Mr Trump's hotels in New York, Chicago and Doral, Florida, the Trump-branded ice rinks had not suffered declines since Mr Trump ran for office.

In fact, their income had risen about 12 percent from 2015 to 2018, according to figures provided by New York City. That was roughly in line with trends at other popular rinks in the city.

“I'm not going to not go because it's Donald Trump . . . even though I hate him and I don't want him to be my president,” said Amy Townsend, 57, a visitor from Los Angeles who was walking in the park this week. She also said that even a Trump-branded ice rink wouldn't dissuade her from skating: “If I want to ice skate in this beautiful area, I'm going to do that.”

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The Wollman Rink played a significant role in the creation of Mr Trump as a local and national celebrity. In the 1980s, the city was mired in an over-budget, long-delayed renovation project.

Mr Trump, then known as a playboy real estate developer, offered to take the project over. He did, and finished it ahead of schedule. In return, Mr Trump got the valuable concession to run the rink - and a national reputation, as a businessman who talked big and got results.

“This is the first time he's famous not for his nightlife, but for improving urban civic life,” said Mitchell Moss, a professor of urban policy and planning at New York University.

“You know what this tells me?” Ms Moss said of the removal of the Trump-branded signs. “He's a businessman. He knows the name Wollman [Rink] is better without Trump.”