Mr. Cohen, who became GameStop’s chairman in June, is one of several company insiders who now use cryptic tweets or memes that drum up interest in their companies or generate cult-like followings online in forums such as Reddit’s WallStreetBets. They include Tesla Inc.’s TSLA -1.41% Elon Musk and AMC Entertainment Inc.’s Adam Aron, who are now known, respectively, in the online communities as “Daddy Elon” and “The Silverback.” Mr. Cohen goes by “Papa Cohen.”

Their social-media strategies are risky but can be effective: GameStop’s share price remains up almost 1,000% for the year. Tesla, too, even while its stock is nearly flat in 2021, still has a market capitalization of roughly $700 billion—more than five times the market cap of General Motors Co. and Ford Motor Co. combined. AMC, meanwhile, watched its stock soar roughly 1,800% year-to-date, helping the movie-theater chain stave off bankruptcy.

Just 10 years ago, it’s hard to imagine that any executive would want to be labeled a meme lord. Corporate America has always relished having larger-than-life leaders, such as Berkshire Hathaway Inc.’s Warren Buffett and General Electric Co. ’s Jack Welch. Yet even the most dynamic ones have long struggled to make any meaningful connections online, preferring to leave a carefully curated social-media image to online marketing teams. Historical precedent—including tangles with financial regulators—made, for some executives, the case for laying low.