He will keep this call sign for the duration of the incident or until his company is re-assigned. For the dispatcher, ICS makes life much easier. All communications from the scene go through Command, so the dispatcher only talks to one person, not twenty. Command talks to dispatch and to four or five captains who are looking after sectors. The captains only talk to Command and to the four or five firefighters who are members of his company.
Confusion is minimized and increased productivity and safety are the benefits.