It was ‘Swallows Yard’ on the 1851 O.S. map [ https://is.gd/tvFS1L ]* but was unnamed on later maps.
By the time of the 1891 Census the name had changed to “Atkinsons Yard”.
Kirklees Image Archive have a photo of it taken c. 1910 [ https://is.gd/Quv4Lq ]
On this map of the same period [ https://is.gd/yb1zZ6 ] the entrance to the yard is below the ‘R’ in ‘LOWER’.
The aerial view to the right shows the area as it is now.
*Click the white rectangle below “contact us”; then click the ‘minus’ sign top left on the map 3 times.