Lynch's full name is not revealed in game, but is revealed in Hitman: Absolution (2012) as "James Seth Lynch". Kane's full name is revealed in the game's manual, as "Adam "Kane" Marcus."
Although, not directly stated, Kane's son died at the age of four when he got a hold of Kane's gun. When Kane is incapacitated, you can hear his wife mention something about Kane keeping a gun in the house.
Kane mentions two other prisoners in addition to Rific, Shelly and Thapa; "Grimley" and "Madsen". They are named after producer of the game Hugh Grimley and lead animator Martin Madsen.