No, the airlines decide the callsigns. Some will be exactly the same as the flight number and others may vary if the airline is attempting to reduce confusion. Callsign confusion is a very serious problem and many airlines have experimented with different callsigns, usually a combination of letters and numbers. Sometimes it works, sometimes it doesn't! Even callsigns which are actual flight numbers may have letters added for the benefit of the airline. Eg is a flight is delayed from yesterday it may have the same number with a letter added at the end.
The callsign and fligh number for a particular scheduled flight will be the same every day. The callsign may change if dangerous confusion arises.