I changed both my name and my gender marker with Social Security today! While your Social card doesn't have a gender marker, there's a sex marker on the application, so I changed mine to 'F.' I brought my letter from my endocrinologist, and the man who handled my application was super nice about everything, and circled the 'F' to show me it had changed along with my name. This is the first time I've officially listed myself as 'female' in any of my documentation. It feels so amazing.