The Rolling Stones' new album, Hackney Diamonds, contains 11 original tracks and a cover of the song that gave them their name.
Producer Andrew Watt suggested that Mick Jagger and Keith Richards do an acoustic version of Muddy Waters' "Rollin' Stone," which they renamed "Rolling Stone Blues."
That meeting took place on October 17th, 1961 when Watt, Mick and Keith ran into each other at the Dartford railway station outside London, and that was one of the records Mick was carrying.
As for his, it became the name of the band, Keith says guitarist Brian Jones was on a call with a writer from Jazz News who asked him what the name of the band was. Jones saw a Muddy Waters album on the floor that contained that song and that was his answer.
"Rollin' Stone" is also reportedly why Bob Dylan titled his 1965 song, "Like a Rolling Stone." And, ironically, Mick Jagger tries to emulate Dylan when recording with Andrew Watt saying if he doesn't achieve his goal, Mick and Keith will say, "It’s not Dylan enough.
“It’s anti-singing, it’s almost speaking; [Mick] has such attention to detail in his voice, of making it not too good. That’s so cool. Every other singer I’ve worked with is like: I can sing that better. He’s the opposite: I could throw that away.”
The Stones covered "Like a Rolling Stone" on their 1995 live album, Stripped.
Source: RollingStones.com and Premiere