Stephen Cashman, 25, an engineering technician, died at HM Naval Base Clyde, known as Faslane, just outside the town of Helensburgh, Argyll and Bute, on Thursday December 9.
Police Scotland are investigating the death, first notified at 12.30pm and thought to have been in the barracks.
A post-mortem examination will be carried out.
A Royal Navy spokesman said: "It is with great sadness that we can confirm engineering technician Stephen Cashman died on Thursday December 9.
"Our thoughts and sympathies are with Stephen's family and friends at this difficult time and we request their privacy is respected."
A Police Scotland spokeswoman said: "A post-mortem examination will be carried out to establish the exact cause of death which is currently being treated as unexplained.
"A report will be submitted to the procurator fiscal."
Faslane is home to the UK's four nuclear submarines, HMS Vengeance, Vanguard, Vigilant and Victorious, which together operate the country's continuous at-sea deterrent."
The Royal Navy Astute class vessels, the First Mine Counter Measures Squadron, Fleet Operational Sea Training (Submarines), 43 Commando Fleet Protection Group Royal Marines and the Northern Diving Group are also based here.
Around 6,800 personnel are based at the site.