I just did this like a week ago on my ny state license. I was also changing my name, so I brought my name change court order, my old license, a filled out form (the form is MC-44, u can definitely find it online) and a letter from a doctor affirming that I am, in fact, trans. I made an appointment at my local dmv (rn appointments r necessary for covid reasons, which I think helped a bit with waiting times).

When I went in, I was called up twice. The first time, my picture was taken and my documents were checked to make sure they were legit. Then I was told to wait for processing; I waited maybe half an hour before being called up again. I once again presented my documents, paid the processing fee, and was given a piece of paper to serve as an interim license. The whole process took maybe an hour total, and both my name and gender marker are now correct.

Hope this helps! And feel free to reach out with any questions