You can use the os.path module to return the basename (filename).
import os
Input = r'\\ITDNAS\MapLibrary\Photos\RRpics\058721Nn.jpg'
filename = os.path.basename(Input)
the filename variable will return '058721Nn.jpg'In this case it would be much better to use an update cursor than the field calculator. In fact, I don't ever use the field calculator because cursors are way easier.
import arcpy, os
fc = r'path\to\your\featureClass'
rows = arcpy.UpdateCursor(fc)
for row in rows:
row.FieldToUpdate = str(os.path.basename(row.PicForward))
rows.updateRow(row)
Make sure to change the FieldToUpdate to your field name that you want to update.