Less than an hour after President Trump named John R. Bolton as his new national security adviser on Thursday, Mr. Bolton made an appearance in the venue where many Americans, including Mr. Trump, have come to know him over the past decade: Fox News.

“I think I still am a Fox News contributor,” Mr. Bolton, laughing, told the host Martha MacCallum at the start of a previously scheduled interview.

“No,” Ms. MacCallum clarified. “You’re not.”

You can’t blame him for being a bit confused.

Mr. Bolton — a featured commentator on Fox News since 2007, after his term as ambassador to the United Nations — is the third TV personality in the past eight days to join Mr. Trump’s it-came-from-the-small-screen White House team.

The president last week tapped Larry Kudlow, the CNBC commentator, to be his chief economic adviser. On Monday, he hired Joseph E. diGenova, a Washington lawyer who drew Mr. Trump’s attention on Fox News, where he described — without evidence — “a brazen plot” by F.B.I. agents to frame the president for a crime.