I've collected together all the maps I can find on the area and it is not named.
One map has Barrow cut through by Roman rd on it, J Britton.
Another has The Girt Bank refering to the large bank that abutts the road next to it. AC Smith
The lane next it is known localy as Gunsight alley because there used to be a firing range there during the war.
One map has the spring next to it named as Swallowhead.
PeteG