Trump called Pompeo 'My Mike' when he worked for him, and the ex-secretary of state wondered in his new book if he'd ever earn a new nickname

• Trump is famous for giving the people in his life nicknames.
• He would call Mike Pompeo "My Mike." Pompeo's friends called him "Pomps."

Former President Donald Trump is famous for calling people by nicknames he comes up with, many of which stick or get under his opponents' skin.

But he had a simple one for Mike Pompeo, his former CIA director and Secretary of State. He called him "My Mike."

Pompeo revealed what he called Trump's "favorable" nickname for him in his new book, "Never Give an Inch: Fighting for the America I Love," out Tuesday.

"The president often called me 'My Mike,'" he wrote. "I still don't completely understand why he chose this unusual locution, which he has also used with others. But it was better than man other nicknames Donald Trump has bestowed on people."

He then went on to muse that Trump might eventually call him something different. Pompeo is considering running for the 2024 Republican nomination for president, which would pit him against Trump, the only person to have officially declared he's running for the White House.

"Perhaps, one day, I'll get an updated moniker," Pompeo wrote in his book. Earlier in his memoir he revealed his friends used to call him "Pomps."

During his 2016 race for the White House, Trump gave many of his opponents derisive nicknames. He called Republican Sen. Ted Cruz of Texas "Lyin' Ted," former GOP Gov. Jeb Bush of Florida "Low Energy Jeb," and Hillary Clinton "Crooked Hillary."

But the 2020 name he had for Joe Biden, "Sleepy Joe," wasn't enough to defeat him.

Pompeo also detailed in his book how Trump had to explain the "Little Rocket Man" nickname to Kim Jon Un, because he didn't know who the British singer Elton John was.

"Never Give an Inch" presents a friendly relationship between Trump and Pompeo, and in it the former official denies that he tried to have Trump removed from office.

Promoting his book on Tuesday on CBS Mornings, Pompeo said he and his wife will make a decision about a 2024 run "in the next handful of months" and that Trump's decision to run again wouldn't affect his choice.