Perhaps predictably, Beacon Hill gets its name because the Puritan settlers placed a beacon on the hilltop. 'Beacon' here essentially meant 'a bucket full of pitch hanging from a pole'. The idea being it could be lit to warn the countryside if the town was attacked - simple, effective, and never actually used.
The hill is shorter today than it used to be - the top of it was carted off to fill in Mill Pond. This had the advantage of making the hilltop easier to build on, and creating more land at Mill Pond - a 2-for-1 deal for developers.
Beacon Hill became THE place to live in Boston after the new Massachusetts State House opened here in 1790. Developers created upscale housing on the south side of the hill, which overlooks the Boston Common.
The North side of the hill had been settled earlier, and was much less posh, sometimes going by the evocative nickname of 'Mount Whoredom'. What a magical address. George Washington, ever the politician, would refer to it in one of his letters as "Mount Horam" - though that sounds more like an instruction than a place.