Why is my power steering pump still screaming?

Did you also replace the hoses ( high pressure and return hose), it would not be a bad idea in doing so.
Can you explain in more detail why you first replaced the pump ? Have you done any other diagnosis on other related components such as rack and pinion?

if not alternator ,power steer pump,air con ,water pump \
serp belt tensioner or idle pullys

check crank pully is not running out of true

could be serp belt squeal
replace the serp belt

Rack or steering wheel might not have been centered when installed. How long ago was it done? Bring it back!

could be worn drive belts, try sprayin the alternator etc drive belt with wd40 before starting and see if no screaming ,if no sctreaming change belts, as these are never changed at the requried intervals

Possible power steering pump failure

You have a bad hose somewhere. I would start at the power steering pump and follow each hose to find the leak. It is probably on the high pressure side, but to be sure you will have to check both the hoses. It will either be at a connection, or at the rack and pinion unit. I would recommend that you use some power steering fluid that contains stop leak, and that may resolve your issue. You will still want to address the leak because power steering fluid is combustible and could catch fire if it gets on the exhaust manifold.

Did you check your fluid level? Sometimes when the fluid level is low it will make that screaming noise.

Check the alignment of your pullys -- one of them is not lined up properly -- most times it is the power steering pully.

If it happens mainly when your car is cold, it is a common symptom known as "morning sickness" or "black rack disease". Check your power steering fluid to see if it has become discoloured. If so, try flushing the system and replace the fluid with an approved power steering fluid. If this does not solve the problem, you may need to replace the rack and pinion steering unit.