Barge
In telephony, barge (or call barge) is a supervisor joining a live call between an agent and a caller so that all three parties can hear and speak.
Also called: call barge, supervisor barge
Barge sits at the top of a ladder of supervision features. Monitor lets a supervisor listen silently. Whisper lets them speak to the agent without the caller hearing. Barge puts them into the conversation openly.
In an AI receptionist the "agent" is the AI, so barging means a person from the business joining a call the AI is handling, the "join" in barge, steer and join.
Do not confuse this with barge-in, which describes the caller interrupting an automated system mid-sentence. The words are nearly identical and the meanings unrelated.