Apparently it's called the referee's crease - I didn't know there was a name for it!
From NHL officials rules:
A misconduct penalty shall be imposed on any player or players who, except for the purpose of taking their positions on the penalty bench, enter or remain in the Referee’s crease while he is reporting to or consulting with any game official including Linesmen, Timekeeper, Penalty Timekeeper, Official Scorer or Announcer.