Craig Nelson, who was also known as Craig Preston, was found at the Woodhead Tunnels off the A628 in Derbyshire at 11:00 BST on Monday.
A post-mortem found the 34-year-old from Wath-Upon-Dearn in Rotherham died as a result of head injuries.
A man, 41, and a woman, 23, were arrested in Sheffield by South Yorkshire Police and remain in custody.
Police have arrested two people on suspicion of murder after a man's body was found on moorland.