"In its meeting today, the board voted to change the front of the building's facade to read 'The John F Kennedy Center for the Performing Arts Restored and Renovated By President Donald J. Trump,' and renamed the physical site 'the President Donald J Trump Plaza,'" said Democratic US Representative Joyce Beatty, a member on the centre's board.
The Kennedy Center and the White House did not immediately reply to requests for comment, although a second source with knowledge of the situation confirmed the board's decision.
The New York Times reported earlier on Thursday that the board passed a resolution "that the Center desires to recognise and honour President Trump's existential and unprecedented contributions to the survival of the Center by all legal means".
The board, dominated by Trump appointees, also voted to close the Kennedy Center for two years, according to Beatty, who sued the Trump administration and the centre over what she called an unlawful name change and the planned closure.
The Trump administration in December added his name to the facade of the Kennedy Center. But in May a judge ordered the removal of Trump's name, ruling the Washington venue cannot be renamed without an act of Congress.
US District Judge Christopher Cooper said in the ruling: "The Kennedy Center's organic statute makes crystal clear that the Center is to be named for President Kennedy, and it cannot bear any other formal name or public memorial based on the Board's unilateral say-so."
Cooper also said, however, that the board has "wide discretion" to make operational decisions about the Kennedy Center, including potentially closing it for renovations following a valid vote.
A federal appeals court in July denied the administration's bid to keep Trump's name on the building while it pursues court action to restore it. Workers stripped Trump's name from the Kennedy Center in June.
The Trump administration argued removing his name would hurt fundraising and worsen the centre's finances.
The appeals court said those claims were not supported by specific facts or evidence.
