Ms. Trump’s defenders have described the backlash against her as unfair and even sexist. Her critics have argued that her role as an adviser to her father has made her fair game.

When Ms. Trump stepped away from her namesake label, her representatives highlighted the move as evidence of her commitment to distance herself from her business. But she retained a financial interest in the brand through a trust that gave her the authority to approve new deals.

The arrangement raised questions about whether she had gone far enough to separate herself from her business. Recent financial disclosures show that Ms. Trump earned more than $5 million tied to her brand last year.

[Read our article examining the financial disclosures filed by Ms. Trump and her husband, Jared Kushner, for 2017.]

Ms. Klem, the brand’s president, said that operating under such scrutiny and restraints had hampered the brand’s growth potential and had contributed to the decision to wind down the company. As an example, she cited a tentative agreement with the Japanese apparel giant Sanei International, whose primary shareholder is a bank owned by the Japanese government, that fell through after The New York Times reported on the deal.

The brand has made some headway expanding overseas. In May, China awarded Ms. Trump several new trademarks. She plans to continue to seek additional trademarks to prevent others from profiting off her name, her spokesman said.

Two people close to Ms. Trump said the main reason she had decided to close down the company was the difficulty it faced in promoting a brand so closely associated with her while she worked in the White House.