I want to find out who the case worker ( CPS) worker is for my 5 year old niece that lives in Long island. If I call the main number and identify myself and why I am calling, do they generally put you through to the child's case worker ?

Typically, you'll not receive any information pertaining to the caseworker for obvious reasons. With your niece being in Child Protective Services, I can honestly tell you (As a "child of the state") that they take confidentiality to a VERY extreme level. When I entered into CPS it was because my father had kicked me out at 12, and I went to my mothers house, who was ordered to never see us again by the court that caused me to stay with an abusive father, then when they found out I was at her house, they came and grabbed myself,a and my brother with no notice whatsoever, and started tripping us around the state with no information given to anyone in our family, not even aunts or uncles. Granted, our upbringing was probably one of the worst that they'd ever heard of , but I don' think that circumstances matter.
Your best bet, in my opinion madam would be to go to your local office, or better yet,t the local office for the county that she was adopted into the system, and request to speak to the director, from there, they will "deem" whether you'll be allowed to have any further contact with your niece.
Good luck, and best wishes to you and your niece.
Greg