Released earlier this month on PC, and earlier today on Xbox One, Fallout 4 Update 1.6 is now live on PlayStation 4.
Adding ExitSave, 300 more names for Codsworth to say, stability and performance improvements, and bug fixes, here’s the full list of patch notes for Update 1.6 (should show up as 1.08 on your console):

New Features

ExitSave – Exiting to the Main Menu or Desktop (PC only) will create an ExitSave. During next play session, the ExitSave will delete itself after you load it. The Exitsave works in all difficulty levels including Survival.
New Add On specific icons in Workshop mode
More than 300 new player names added to Codsworth’s vocabulary
Support for upcoming Add Ons

Fixes

General stability and performance improvements Fixed a crash related to targeting an enemy weapon while in VATS
Fixed an issue where a Companion would become stuck walking and unable to run
Fixed issue in “Mankind Redefined” to prevent the player from getting stuck in elevators while in Mass Fusion Building
In “Boston After Dark” quest now completes properly when waiting for Old Man Stockton
Fixed occasional issue where player would become permanently invisible
Dead settlers can no longer be commanded or assigned to supply lines
Fixed issue where deleting saved games would cause other saves to disappear
Fixed occasional issues with activating mods that did not come from Bethesda.net
Minor bug fixes and optimizations to Mods load order and browsi...