#Your interpretation is accurate.
Your interpretation is accurate.
Though in many groups this is not exactly how it is played out (some tend to allow a surprise round to take place sort of out-of-order before rolling initiative for everyone else), the rules as written make it clear that at the beginning of a combat, all creatures should roll for initiative and have a place in the turn order, even if they are surprised and therefore will not actively do anything in the first round; thus the troll gets a turn during the surprise round on which it takes no actions and does not move. If it has already taken damage, that damage will start regenerating, since as you correctly note, regeneration is a passive ability, not an action or reaction of any kind that the troll must specifically take.