Last July, after my legal name change, I went to the SSA and they accepted my California DL with my new name and photo as ID. California allows the DL to be changed with just a form and a doctors letter indicating that the process of gender change is underway. It allows the female designation immediately and name change on the DL without a court order. Further they gave me my old DL with a hole punched in the exp date. I never had to use the old one.
Then the clerk looked at my court order, entered the info including the case number and my name was changed. She had the court order that gave my old name (which matched the SSA records) and new name. I showed a valid Photo ID. So the clerk had the complete linkage of my identity and their records.
I asked her to change the gender marker to female and she tried but the software asked for evidence of a surgeon's letter for gender reassignment surgery. She told me to come back with the letter after surgery and she would change the marker. Other than that, there was no talk about my mismatching female name and gender.
In two weeks, I received a letter from the SSA with my new SS card and new name.
I think that Julie was given the runaround by clerks who were deliberately trying to cause trouble. Clearly one can have a female name and a male marker. I happened for me six months ago.