Sorry if this feature is already in-game, I didn't found it... Day and Night Cycles would be good, depending on our departure time, the cycle could change... The ability to choose when starting (at night or day depending on the hour of the day) could be a nice selection.
If you mean staying overnight in game, I believe it is currently not possible due to technical limits. The game can only simulate one single day from 00:00 to 23:59. While you can stay in the game after 23:59, no train will start moving and no more new trains will spawn. You will have to load the game again for late night or early morning services. Other than that, we already have a time system with seasons. You can see the sun rising in a morning service, and it rises earlier in summer.