Nobody really knows where 'Shepherd's Bush' comes from.
It is thought that shepherds rested their flocks on the common land here on their way to Smithfield Market in the City. Another idea is that it was named after someone in the area called Sheppard: in 1635 the place was recorded as Sheppard's Bush Green. That common survives as Shepherd's Bush Green, a triangle of grass ringed by roads.