Each contractor who enters into a state contract with the state for ten thousand dollars ($10,000) or more, shall be assigned an identification number by the department. Each contractor who has been assigned a number, shall list it on each contract he or she enters into with the state, regardless of the amount of the contract. In the case of a corporation or firm, the president’s assigned number shall be used exclusively on each contract. The assigned number shall remain unchanged regardless of future name changes.