It was around noon on Friday, June 28, when Kim Kardashian West realized it was time to cave. After three days of being globally thrashed, she would have to change the name of her latest venture, a shapewear and lingerie line, a concept she had been thinking about for the past decade—longer than she had been married to Kanye West, longer than her four kids had been alive, longer than she had been arguably the most famous woman in the world other than Queen Elizabeth II. The name Kimono had to go.

So the team of investors and...