Now, I grew up just 12 miles from Winchester, so I'd heard of Sleepers Hill. I'd always assumed that its name alluded to a legend about mythical heroes-in-waiting, or at the very least a nest of indiscreet Russian spies. Apparently, however, it refers to the trees that used to grow at the top, which were chopped down to make railway sleepers for the line running from Winchester to Southampton. Quite interesting from an industrial archaeology point of view, I suppose, but a little prosaic.
The next hill along is called Oliver's Battery. As a child I was told this name commemorated a Civil War gun emplacement. Perhaps though it will turn out to memorialize an electrical supply shop run by Mr Oliver?
Sometimes it's better not to ask.