Where else can I look? (US-NY)

My father is adopted. I have the name he was given at birth (from birth mom), where he was born, his name (from my grandma), as well as the date of the adoption being finalized. According to my mom, because his adoption took place in 1964-1965 they could have transported the birth mother here from another state as well as allowed her to choose any random name- something grabbed from a newspaper.

I recently did Ancestry DNA and am still awaiting results. I already worry I'll feel a crushing sense of disappointment if nothing comes up, and it will be multiplied by the fact that my dad knows I did it and has asked for info 😔

He doesn't want a relationship with bio family, I'm not sure if or what I may want, but we definitely want medical information.

I am in NY state and am curious what else I can do or where else I can look. Would I (as neither the adoptee, adopter, or bio fam) have a right to request this information?