Michael Delaney, 48, died in hospital after being found lying seriously injured on the town's Drumbathie Road.
It is believed that he had been struck by a vehicle.
Sergeant David Stenhouse of Road Policing at Motherwell, said: "We are still trying to trace the vehicle and driver involved. I would re-appeal to anyone who was in the area and heard or saw something to come forward."
Anyone with information should contact Road Policing at Motherwell on the non emergency number 101 orCrimestoppers on 0800 555 111