In 1660, King Charles II desired to be able to walk from Hyde Park to St. James's Park without having to take his feet off royal soil. He was really down to earth like that. He commissioned the creation of what he called Upper St. James's Park to bridge the unroyal gap between the aforementioned parks.
The park was officially renamed Green Park in 1746 - an explanation for the name change comes from an probably untrue story: when Queen Catherine discovered that King Charles had picked flowers from the park to give to another woman, she ordered the flower beds in the park to be removed in a fit of jealousy, making the park entirely "green." To this day there are no flower beds in the park.
Personally, I'm more concerned that he was picking flowers out of a park to give some woman. What's the matter, mate? Can't find a florist?
In June 1840, Edward Oxford attempted to assassinate Queen Victoria as her carriage passed just outside Green Park. He fired twice on the carriage, missed, and was subdued. This was the first of eight attempts on the Queen's life. She was pregnant at the time.