The 34-year-old, from Wath-Upon-Dearne, Rotherham, was found at the Woodhead Tunnels off the A628 on Monday.
Post-mortem tests found he died from head injuries and Derbyshire Police has launched a murder investigation.
The force is appealing for information on Mr Nelson's movements in the days before the discovery of his body.
A man whose body was discovered on moorland has been named by police as Craig Nelson, also known as Craig Preston.