It's a common misconception that the nickname 'slowhand' was given to Eric Clapton for his ability to play the guitar slowly. When you think about it, anyone can play slowly but some are just a lot better at it than others.
Eric Clapton got his nickname dating back to when he was performing with the Yardbirds in 1964. Usually when a guitarist breaks a string onstage during a performance, a roadie will take the guitar and immediately replace it with an already strung and tuned guitar, then restring and tune the first guitar off-stage. Clapton's habit was to change the string and tune it while standing onstage. During one particular concert while Clapton was changing a string, the audience began a slow hand clap or a 'slow hand' until he began playing again.
The manager of the Yardbirds, Giorgio Gomelsky, coined the nickname 'Slowhand' from that 1964 concert.