US District Judge Christopher Cooper in Washington DC directed Trump's administration to take down all physical signage bearing the current president's name and to eliminate any references to a "Trump Kennedy Center" from official materials within 14 days.
"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 wrote.
"Congress gave the Kennedy Center its name, and only Congress can change it."
The judge added: "(The) court does not purport to dictate how the Center should be run, nor does it prescribe any particular plan for the institution - construction, closure, or otherwise - moving forward."
Cooper ruled in a lawsuit brought by Ohio Democratic US representative Joyce Beatty, a member of the Kennedy Center's board by virtue of her position in Congress.
The White House did not immediately respond to a request for comment.
Cooper's order also stops the administration's planned two-year closure of the building.
The judge said his order does not prevent the Kennedy Center from moving forward with planned capital repair work that the record in the lawsuit "demonstrates is sorely needed".
Trump installed a handpicked board for Kennedy Center that then named him chairman.
His name was then added to the facade of the Kennedy Center, which was opened in 1971 as a living memorial to the late president John F Kennedy.
Trump's plan to renovate the centre is part of a broader push by the Republican leader to reshape Washington DC's monumental core.
He also intends to erect a 76-metre arch and to build a ballroom at the site of the demolished East Wing of the White House.
Those efforts also face court challenges.
A federal appeals court has allowed Trump's administration to move ahead with building the ballroom as it considers the case.
with AP
