Tomasz Dzieciol, 34, of no fixed address, appeared at Wolverhampton Crown Court today and his sentencing was adjourned until March 25.
It comes after a man, believed to be in his 40s, was found with head injuries in the alleyway off High Street on December 17, 2019.
Police cordoned off Rutland Passage, near Lloyds Bank and The Full Moon pub, at around 6.20pm.
Officers remained at the scene overnight as an investigation got under way.
Rutland Passage leads from the high street to King Street.