Despite the name, the complex is not owned by Mr. Trump, and the various buildings are run by distinct entities. 180, 160 and 140 Riverside Boulevard are rental buildings owned by Equity Residential, a Chicago-based company that acquired them for $809 million in 2005, and contracted with the Trump Organization to use the Trump name. The three others, 120, 200 and 220, are condominiums. 200 paid Mr. Trump $1 to use his name on the building, according to reports.

In 2016, hundreds of tenants at 180, 160 and 140 Riverside Boulevard signed a petition to Dump the Trump Name, and it was removed three weeks before he took office. At the time, Equity said it was not a political move: the contract with Mr. Trump to use his name on the buildings had simply run out.

When 200 Riverside Boulevard tried to follow suit, the condo board went to the State Supreme Court to determine if it had the right to remove the name, which the Trump Organization said was inviolable. Judge Eileen Bransten ruled in the board’s favor, saying the letters could be stripped from the 46-story building, pending a vote by the tenants.

The last holdout, 220, hung on, not because of any fealty to the president, but because they feared litigation, according to a resident who asked that her name not be used because she did not want to anger her neighbors by discussing internal building politics.

“When 200 did it, it set a precedent; we saw what was possible,” she said. “Most people were like-minded in wanting it to come down, but there was a little bit of fear of what is going to happen, what sort of backlash there would be.”

“We lived here well before we ever dreamed he would be president, but in the last two years it’s been really awkward,” the 220 resident added. “When a cab pulls up in front our building, the cabdriver always says, ‘Ugh, Trump!’”

The boards of the two buildings that announced the removals this week could not be reached. The Trump Organization did not respond to an email requesting comment.