Yes, you must change your drivers license in NY within 30 days of moving to NY. Same goes for your insurance. You can then change it back to CA when you move back there.
Welcome to New York.
I suggest that you read: http://www.nydmv.state.ny.us/resident.htm
I also suggest you read: http://www.nydmv.state.ny.us/license.htm#driversmoving
I hope that you find the above limks helpful and that you enjoy your time here in New York.
George P . Conway
Sign up to receive a 3-part series of useful information and legal advice about DUIs.