Need Help With Lien Holder Not Updating My Name In California

I (27nb) have my car financed through Toyota Financial(TF). Last August, I finally got my name legally changed and all my identifying documents updated.
For the last 4 months, I have been going back and forth with the DMV and TF to try and get my car’s registration updated with my new legal name.
TF first said that I had to go through the DMV. So I went to the DMV, and they told me that the lien holder has to change it since they still hold the title. When I went back to TF, they tried to say that they can’t update it at all. Then they said they could only update the registration once i pay off my car in full. I don’t have a spare $7k lying around, so that is not an option for me.
As a queer person, I am already so scared of getting pulled over. Now even more so as none of my identification matches my registration.
Do I have a case here?
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