Two attorneys with knowledge of the case say Dale Andrew Hayden was the driver in last week's crash that also left 17 people injured.
They spoke on condition of anonymity because they are not authorized to release the information publicly.
The San Antonio Express-News, which first reported Hayden's name, says the 50-year-old is a military veteran.
Hayden's attorney, Hal Brockett, did not immediately return a message seeking comment Tuesday.
The National Transportation Safety Board says oilfield services company Smith Industries owns the truck involved in the crash in Midland.
On Tuesday, federal investigators plan to re-enact the events that led up to the collision.