Simon Lee Follos, aged 49, was found unresponsive at Stoke Heath Prison, near Market Drayton, on August 22 this year.
The Prisons and Probation Ombudsman will investigate the circumstances, it has been confirmed.
An inquest into his death was opened at Shirehall. The hearing was told that paramedics and the police were called, but Mr Follos, who was born in Dudley and lived in Galbraith Close, Coseley, did not respond to resuscitation attempts. He was pronounced dead at the scene and his body was identified by prison staff.
John Ellery, senior coroner for Shropshire, Telford and Wrekin, adjourned the hearing for a pre-inquest review on December 15. A full inquest is expected to be held at a later date when investigations have concluded.
A Ministry of Justice spokeswoman said: “Prisoner Simon Follos died at HMP Stoke Heath on August 22, 2023. As with all deaths in custody, the Prisons and Probation Ombudsman will investigate.”