Well, a quick fix may be to look up the requirements and cost of a name change where you live and inform her. "I could change my name, but I'll need $300 total to get it updated with the courts and then to change all of the documents that I'd need to pay for. I'd also want to save an extra $200 while my bank account and credit cards are being updated just in case there are any issues."
Sometimes people don't realize that there are costs associated with things because they've either never done them or haven't done them in a long time. My parents didn't understand initially why I had waited so long to start HRT, but when I showed them how much insurance pays towards my lab work, they understood - part of why I had waited was to save $500 on annual labwork, as my old insurance wouldn't have covered anything.