The whine is usually created by a problem with the power steering fluid that the pump is trying to move. If you've kept up with regular maintenance on your car including changing your power steering fluid as recommended, then the whine is most likely due to air bubbles in your system.
Did you replace the reservoir when you replaced the pump? If not you need to check in the bottom of the reservoir there maybe a screen that gets clogged over time. You’ll need to empty the reservoir to confirm this and if it’s clogged remove the reservoir and blow it out with compressed air and brake cleaner.
You may have air in the system. The reservoir oil should gravitate into the pump. There can be vehicles where the reservoir is below the pump and not very common but it adds another level of difficulty where you would have to fill the suction line to the pump and hopefully there is a check valve on the end of the pickup. Can you park the vehicle on a slope to make sure the reservoir is above the pump?
Open the top of the power steering pump reservoir. Siphon the power steering fluid out, using the turkey baster or other siphoning device. Place shop rags under the hoses at the back of the power steering pump.
Slide the drain pan under the hoses.
Remove the high and low pressure hoses, using the appropriate line wrench. Allow the hoses to drain into the drain pan. Unplug the wiring harness connector, if applicable to your year, make and model.
Well, I would check fluid level first. If level is good and there is no even seemingly minor leaks, take the belt off and see how much play is in the pulley. If none, how is the belt? If those are dandy, I would look at steering components.