John Leonard Scollay, from Lerwick, Shetland, died after the Diamond fishing boat went down in the early hours.
Shetland Coastguard received a mayday call from the Diamond reporting that it had hit rocks and was going over at around 2.55am today.
A second man was recovered by the Aith RNLI lifeboat and is said to be in a stable condition.
Both men had been taken by Coastguard helicopter to the Gilbert Bain Hospital on Shetland.
A report will be sent to the procurator fiscal.