The 46-year-old actor told the YES Network show CenterStage that before Ryder landed her first major role, he came up with the name.
"We were listening to The Doors, to 'Riders on the Storm'," he explained. "[Winona's] real name is Horowitz, and I said, 'You know, I'm thinking Winona Ryder sounds cool', and she was like, 'Yeah!'"
However, Sheen added that Ryder has refused to acknowledge his contribution.
"[She] never, never gave me credit to this day!" he joked.
The Anger Management star also spoke about his abrupt exit from Two and a Half Men last year, following his public denouncement of show creator Chuck Lorre.
"A lot of it was my fault, a lot of it was their fault," he said. "They went into my personal space, you know? And then my personal space might have been not the most private place in the world."
Sheen admitted that his playboy lifestyle also played a part in the show's decision to axe him.
"It got in the way of the work," he added. "I like to think that I didn't get fired, I got traded for a player to be named later."
Watch Charlie Sheen in a promo for Anger Management below: