Change last name on passport

I am a Chinese citizen and I received my Permanent Residency through marriage. My green card has my husband's last name yet my Chinese passport still has my maiden's name. I tried calling the Consulate but nobody seemed to answer the phone.
My question is, I live in Georgia right now, and do I have to go to NY Consulate personally to change my last name on my passport? Can I get it done through mail, or go to Texas Consulate?

Secondly, how long will it take for this process. Is it walk-in and can be done at the same day or I have to stay in NY/ TX for a week for my passport for such process?

Thank you!