He was 56-year-old Brian Wellburn from the Annan area, who was found near a bridge close on the Scotland-England border early last Monday morning.
The southbound carriageway of the motorway was closed for much of the day and diversions put in place.
Cumbria Police, who are seeking witnesses, said emergency services responded to initial reports of an incident at 7.34 am.
A spokesman said: “The exact circumstances of the death are unknown and police are continuing to investigate.”
However, he added that the death was not being treated as suspicious.
The Coroner for Cumbria was being kept informed.
Anyone with information was asked to contact Cumbria Police on 101 or Crimestoppers anonymously on 0800 555 111.