Kevin K. McAleenan, appointed the commissioner of Customs and Border Protection by Mr. Trump in 2018, then took over as the acting secretary of homeland security, but Mr. Trump has not nominated him to permanently run the department. Mr. Homan’s appointment is likely to undercut Mr. McAleenan’s traditional role as the top official responsible for securing the border.

Mr. Vitiello said the president was not helping the Department of Homeland Security by having so many temporary leaders overseeing agencies.

“Whether it’s the department at the cabinet level or the director at ICE or the commissioner at C.B.P., having a confirmed leader, it matters,” Mr. Vitiello said. “It matters in the cabinet meeting. It matters in the interagency discussion. The sooner the work force and individuals involved know their futures are certain the better off it is for everybody.”

Mr. Homan is the third official the president has inserted into Mr. McAleenan’s territory since he became acting secretary. Last month, Mr. Trump named Kenneth T. Cuccinelli II, a former attorney general of Virginia who once advocated an end to birthright citizenship, to lead the United States Citizenship and Immigration Services. And Mr. Trump brought back as the head of ICE Mark Morgan, who was forced to resign as head of the Customs and Border Protection at the beginning of the Trump administration but has also made numerous appearances on Fox News praising the president’s policies.

Mr. Trump said on Friday that he was still not sure whether he would nominate Mr. McAleenan to permanently lead the Department of Homeland Security.

“McAleenan, he is doing a very nice job. We’re going to see,” Mr. Trump said. “I’ve got to get used to him. Because it’s a very important thing to me, the border. We need strong people at the border.”

Mr. Homan fits that description: Burly and blunt-spoken, he comes across on television as the former police officer that he is, focused exclusively on the need to be tough when it comes to keeping immigrants out of the country. But it is not clear what role Mr. Homan will play in developing and carrying out the president’s border policies at the White House. Mr. Miller, the president’s senior adviser and the architect of Mr. Trump’s immigration agenda, remains the most important adviser on the issue.