When it came to naming their third son a few weeks ago, Megan Fox and Brian Austin Green sidestepped traditional boys names like Ethan and Jacob for the gender-agnostic name Journey, which may have been a subtle nod to the couple’s much-chronicled attempts to work their way back from the brink of divorce.

Dax Shepard and Kristen Bell also opted for an indeterminate-sex name (Delta) for their second daughter, born last year. “It was a joke, because our first daughter’s name is Lincoln, which is very masculine,” Mr. Shepard said on “The Ellen DeGeneres Show.” “So a friend of mine teasingly texted me: ‘Oh, great! What’s this one going to be? Navy Seal? Delta Force?’”

Their choice hardly seems unusual in a culture where Heidi Klum, Jessica Simpson and Drew Barrymore have all chosen names for their daughters that could go either way and collectively sound like a frontcourt for the 1962 Detroit Pistons (Lou, for Ms. Klum’s daughter; Maxwell, for Ms. Simpson’s; and Frankie, for Ms. Barrymore’s).

It’s not just Hollywood. At a time when Banana Republic has done away with pink and blue distinctions in a children’s line, some high schools have stopped using graduation gowns with different colors for boys and girls, and unisex is de rigueur in fashion, gender-blurring baby names are on the rise among American parents.