TurboTax wont let me add college tuition payment for my daughter on my NY state return. Only presents with my name as a student wont allow me to enter my daughters name

College did not and will not issue you a 1098 -T because you are not the student.

 To claim the education credit, on the federal return, the student must be your dependent.  If she is, then you enter her 1098-T on your return. 

If you enter the wrong student, you'll have to delete all the info and start over. Go through the entire education interview until you reach a screen titled "Your Education Expenses Summary".  Click delete next to the student's name.  You'll then get the "Your Education Expenses Summary" screen again.  Click the "Add a student" button.

New York also has the dependent requirement. Reference: https://www.tax.ny.gov/pit/credits/college_tuition_credit.htm