How do commercial pilots keep situational awareness of their current call sign?
Some modern airliners have a place where the flight number can be displayed on the cockpit displays. This information can be entered off the dispatch paperwork when setting up the flight plan, and is displayed throughout the flight for easy reference.

For example, you can make out "DLH463" on the screen at the bottom right of this Lufthansa A380 cockpit photo, corresponding to Lufthansa flight 463.

The Boeing 787 has a similar feature:


  The two outboard displays are a fixed format that provides primary
  flight display information combined with an “auxiliary” display that
  consolidates frequently referenced information for the crew, such as
  flight number, each pilot’s microphone-selected radio and its
  frequency, and transponder code.


You can see this on this 787 cockpit photo at the top of the leftmost monitor: "FLT -> BAW787"

(Photos not embedded due to licensing restrictions.)