A Democratic lawmaker has asked a federal judge to prevent the John F. Kennedy Center for the Performing Arts from inscribing President Trump’s name on the building, arguing that the plan is an attempt to circumvent a previous court order.

In a court filing on Tuesday night, lawyers for Representative Joyce Beatty, who is suing the center as an ex officio board member, wrote that the decision by the center’s Trump-allied board was a “childish refusal” to accept an order to remove letters spelling out the president’s name from the building’s marble facade.

Last week, the board voted, instead, on an inscription below the current signage that would read “Restored and Renovated by President Donald J. Trump.” In the same court filing, lawyers for the Kennedy Center wrote that they would not move forward with the project until Sept. 8 “at the earliest.”

Lawyers for Ms. Beatty asked the court to intervene before then.

“This court should not permit defendants to effectuate this latest gambit, in direct contravention of its earlier decision and in naked defiance of the law,” wrote Nathaniel Zelinsky, one of the lawyers representing Ms. Beatty.

In May, Judge Christopher R. Cooper of Federal District Court in Washington ruled that the board’s decision to rename the institution the Trump-Kennedy Center was unlawful, finding that only Congress had the authority to change the center’s name.

Directing the center to remove the letters installed on the marble late last year, Judge Cooper cited a provision in federal law that says “no additional memorials or plaques in the nature of memorials shall be designated or installed in the public areas.” The Kennedy Center took down Mr. Trump’s name in June but is appealing the ruling.

Seeking a workaround that might satisfy the judge, the center’s board approved several options for honoring the president last week, including the inscription. Another idea was to rename the grounds on which the center sits the “President Donald J. Trump Plaza.” The resolution approved by the board directed officials to act under “all legal means.”

The judge will also consider whether to approve the board’s decision last week to move forward with President Trump’s plan to close the center’s main building for two years for a sweeping renovation project that officials say is necessary for the institution to flourish.

In a sworn declaration filed on Tuesday night, Matt Floca, the center’s executive director, wrote that the decision was based on the findings of an independent analyst. The analyst advised board members that keeping parts of the main building open during renovations, funded largely by $257 million allotted by Congress, would “not only increase the cost and length of the project, but would also present substantial safety concerns.”

Ms. Beatty has also objected to the continued presence of tarps, arranged over scaffolding, that have obscured much of the center’s main signage since Mr. Trump’s name was removed.

In his declaration, Mr. Floca wrote that they were there to protect the facade “in light of reported panel damage,” and to facilitate repairs to the building’s roof overhang.