That might not even happen, though. Space isn't like an ocean where you can move around arbitrarily; craft mostly follow ballistic trajectories. As it is, it's actually more like artillery with human cargo than like aviation, let alone a boat that can go anywhere anytime.

The exceptions are craft with slow-burn engines like ion drives, which allow enough delta-V for a craft to hit more than one destination. Those still need energy, though, so they need to be near something like the sun to operate indefinitely. Over interstellar distances, a 20-year boost at millinewtons is still relatively short, and we're back to ballistic trajectories. On such a mission, if the crew is human and awake it would be more a matter of keeping everything operating as intended than deciding anything. I expect any culture that develops would be more about the off-time.

Speaking of boosts, burns and delta-V, you can see a bit of space's own culture growing already. My best guess is that the structure of a future interstellar mission would be a bit familiar to today's ISS astronauts.