Technically, both the bottom and top of these stairs are at different parts of Berkeley Way as it loops back around towards Diamond Heights Boulevard. It's just a lot less confusing to refer to the bottom as being at Diamond Heights Boulevard.
The name Onique is a Spanish translation for onyx, fitting in with the naming scheme in Diamond Heights where many streets have the English names of gemstones, and stairways have the Spanish names.
Built in the 1960s, when Diamond Heights was developed.