He welcomed twins Alexander and Ella with wife Amal Clooney in June.
And George Clooney revealed why they chose classic names for their children, the Daily Mail reported.
The 56-year-old actor said he and his wife "didn't want to have dumb names" for them, according to Paris Match via People.
Adding: "We didn't want to give them one of those ridiculous Hollywood names that don't mean anything."
George told the website that his son and daughter "already have enough difficulty bearing the weight of their celebrity."
The movie star's interview with Paris Match came days after he and Amal stepped out for premiere of the film Suburbicon at the Venice Film Festival.
George spoke to Entertainment Tonight saying that he and Amal, 39, "just didn't want to have really dumb names [for their children]."
The actor added that he and his attorney wife "figured these kids are going to be looked at a lot and watched," so they "wanted them to at least have a break with the names."
George and Amal didn't choose the names Ella and Alexander because of any "great inspiration," he told the website.
He didn't name them after anyone or a historical figure like Alexander the Great or Ella Fitzgerald.
George told ET that his kids, who were born on June 6, don't share the same personality.
While Ella is "elegant" and looks similar to Amal, Alexander is "a moose," adding that he "just sits and eats."
George and Amal are set to celebrate their third wedding anniversary this month; they tied the knot on September 27, 2014.
The actor directed and produced Suburbicon, which is set to hit theaters in the US on October 27; Grant Heslov, Joel Silver and Tedd Schwarzman also co-produced.
The crime comedy stars Matt Damon and Julianne Moore.