I'd contact a family mediator if I were you OP. as I've repeatedly said
You may as well talk to a ward full of patients as us about your life.
Some will say how unfair your gf is, some will say how ridiculous you are not to change your name, as it's 'just your foster mums' anyway' some will say that your relationship is doomed.
Whatever.
The best place to look for a resolution is by listening and talking with your gf.
If you feel so insecure to canvas a group of randoms on the internet about it, well and good, but don't let that influence your decisions or feelings on the matter. As I said you may as well flip a few coins, or pull petals out of daisy: she loves me, she loves me not.
It's your life, what do you want? What does your gf want and what are you going to do to improve the communication in your relationship going forward.
Don't answer me talk with your gf.
Use a mediator if you want to have a more formal arrangement and acknowledgment of your desires, and acknowledgment of hers, and a resolution in a set timeframe.