This is the lower section of Shankill Road.
"Peter's Hill has had its name attributed to one Peter Alexander who kept a Farmers' and Carmens' inn, which is said to have originally stood, on the present site of the Peter's Hill Public Baths, Peter, however, passed to his rest in 1733, so that the origin of the name remains in obscurity. In 1668 John Biggar sold 3¼ acres in the field next to Gill's Land and also the plot of land without North Gate Street, and the next adjoining the grass of the Rampier situate on the north side of the highway leading from the town to Peter's Hill called Goose Lane." (John J. Marshall, Belfast Telegraph, 05/02/1941).
This transaction was mentioned in 1680 in a Corporation meeting but the sale had taken place in 1668, which is too early for the name to be connected with the said Peter Alexander (Young 1892, p. 140). However, it may be the case that Peter's Hill became connected with Peter Alexander in the minds of the Belfast citizenry in the 18th century.
On July 6. 1768. Arthur, Earl of Donegall. made a grant of a parcel of ground in the town of Belfast, on the north side of the street commonly called Carrickfergus-Peter's Hill," quoted by Bardon, pp. 33-34.