My [F26] trans sister [F23] changed her name to my current name.

My sister came out as trans about 2 years ago. We are not close at all. The last time I saw her was at my college graduation 3 years ago. However, when I heard the news, I sent her a text congratulating her and wishing her well. She's always been the black sheep of the family. Interested in different things than me and my family, kind of the "look who came out their cave" energy. She's since left our small town in Western Mass and moved to Seattle.

I currently live in Boston and heard she changed her name. She had a fairly gender-neutral name to begin with and didn't change it initially when she came out. However, 2 months ago I heard from someone who follows her on IG that she changed just her first name to my current first name thus giving her the exact (minus the middle) name as me. I immediately called her and asked why she'd do such a thing. She said she'd "always liked that name" and "couldn't find a better." She went on to say, "We don't really talk, I don't live! on the east coast and never visit, I don't know why this even matters?"

I explained that I'm kind of embarrassed and feel awkward about this and asked to help her choose a different that literally isn't mine. I do go back to my hometown somewhat frequently and so I'll have to deal with this socially with friends and other people we both know when I do end up going back. Anyone from a small town will tell you, word spreads fast. She said she's made up her mind and she intends on sending in the paperwork to change it legally this month. I called my mom and she said she had the same exact conversation with her but my mom lost her patience and had kind of an argument and said something transphobic in the moment and they haven't spoken since. My dad hasn't touched this at all lol.

I'm just not sure what to do here because while it would be nice to be closer to my only sibling, I can't shake that we have the same name. It's weird and annoying tbh. How do I go about getting her to change her mind? Or do you think I can't change her mind?