When does a player become officially disqualified and considered bench personnel?

A player becomes officially disqualified and is considered bench personnel when they are notified by an official. This notification is critical as it formally communicates the decision that the player can no longer participate in the game. The referee or official is responsible for enforcing the rules of the game, and their decision is final and authoritative. Until this communication occurs, the player remains eligible to continue playing, regardless of any unofficial signals or decisions made by others.

The other options lack the necessary authority or formal procedure. The coach's decision does not disqualify a player until an official enforces that decision. Similarly, a player informing the official does not constitute disqualification; it must be an official's determination. Lastly, simply expiring game time does not result in disqualification; players are only removed from play through an official ruling. Thus, the only correct circumstance under which a player is considered disqualified is when the official provides the notification.