Keith Richards on the change of his last name to Richard and then back to Richards:
“It made me sick – my name’s Keith Richards. It hardly makes it against Howlin’ Wolf or Muddy Waters, does it? On my first guitar I had ‘Boy Blue’ written – just pathetic. But that was as good as I got at the time.”

From A Journal of Musical Things:
What’s the last name of the Rolling Stones lead guitarist? Is it “Keith Richards” or “Keith Richard?” The answer is “both.”

Keef was born Keith Richards on December 18, 1943, in Dartford, Kent, the only child of Doris and Herbert Richards. Note the “s” at the end of the name.

He remained Keith Richards until 1963 and the founding of the Rolling Stones. Their manager, Andrew Loog Oldham, a very image- and fashion-conscious guy, had a problem with Keef’s surname.

“That’s not very ‘pop,’ innit,” he said. “Besides, Cliff Richard [an increasingly popular British pop star] does all right with that name, doesn’t he?” Maybe Oldham was thinking that people might assume that this new Stones guy was related to Cliff. That’s never been confirmed, but it does sound like the Oldham would operate.

Keith was amenable to the change. As he later told the BBC:
The Rolling Stones‘ Keith Richards has revealed that he used to hate his name – because he thought it was not cool enough.

“It made me sick – my name’s Keith Richards,” he said. “It hardly makes it against Howlin’ Wolf or Muddy Waters, does it?
On my first guitar, I had Boy Blue written – just pathetic. But that was as good as I got at the time

From that point on, Keef was billed as “Keith Richard” through the rest of the 60s and through the 1970s. Check any original album release from that era and you’ll see him referred by his truncated name.

But then, a change of heart. Sometime around Keef’s arrest on drug possession in Toronto on February 27, 1977, he decided to re-add the “s” to his last name. What precipitated the change or when it exactly happened seems unclear.
(Ref. change of name)