The Dark Beyond The Stars by Frank M. Robinson
Sparrow is a young crewman on a “generational” starship who loses his memory after an attempt on his life. He must piece together what has happened before the killer strikes again.
He learns that the starship has been ranging through the galaxy for 200 years, searching in vain for any form of life. The captain, who is still the original captain who left Earth, has undergone drug therapy to become nearly immortal.
The crew, several generations removed from their Earth ancestors, are evolving into something beyond human that thinks with a hive-mind. The captain is obsessed with his mission and plans to take the starship across one of the empty reaches of space even though the vessel is so broken-down by now that it probably won’t survive the trip. The crew may be forced to mutiny. Watch for the shocking ending. A chilly and cerebral read.