Wiring new range hood exhaust fan motor
The old motor had two hot wires in addition to the white (neutral) so that the SPDT switch could select high or low speed. The new motor is one-speed, though you could replace the switch with a variable speed fan control if you want to adjust the speed and noise level. N.B. The link is just for illustration, that particular control might or might not be suitable.

If you don't mind a one-speed fan., then simply wire one or both switch wires to one black motor lead and the other black motor lead goes to the white (neutral) wire. If you connect both, there will be two ON positions and one OFF, but if you connect the wire for the middle position and cap the other lead, then there would be two OFF settings and one for ON.