The Rolling Stone explained

To save other readers the frustration I felt at trying to decode the title of the Chris Urch play we'll be discussing tonight, "The Rolling Stone," here is the answer: "It was inspired by the name of a Ugandan tabloid newspaper that in 2010 published the names, addresses and photographs of 100 supposedly gay Ugandan men, accompanied by the banner headline “Hang Them.” The paper, which bore no relation to the American music-themed magazine, was in existence for only four months before it was shut down by the Ugandan High Court. But not before a gay rights activist identified in the article was brutally murdered in his home as a result of the exposure."

That information comes from a review in the Hollywood Reporter of a 2019 production of the play. Spoiler alert: The critic was not at all impressed. However, this compilation of reviews of other presentations of "The Rolling Stone" includes some very positive ones.