I would continue to be the voice of reason at home and not go along with any of it, say her friends can call her what they like but you spent a lot of time choosing her name and that is the one you'll be using.
DD has never been into dresses and has always dressed from both the 'pink' and 'blue' sections, had a short hair style due to sensory issues
I had previously worked in a secondary and knew this could rear it's head due to her ASD so spent alot of time dropping in references to more androgenous people like Tilda Swinton etc. locked down her internet usage as ASD teens are drawn to gender ideology as they see it as warm and welcoming when they feel outer of kilter with the world around them opposed to the grooming cult it is.
She dabbled very briefly with it and then like many of my former 'Trans' female students said she was same sex attracted - that was no issue and it died a death from then.
DD has settled on her own style now, more Dark academia than anything lots of Disturbia, shirts and waistcoats in her wardrobe paired with a good smoky cat eye.
In my experience most of my 'Trans' female students were same sex attracted and it wasn't accepted at home and came out later, had experienced SA and it was safer being a 'man', were autistic and confused about the greyness of self expression and felt they needed to be in one box or the other. These students were often in the same friendship groups or same pecking order in different years. Often in class other students would bend over backwards to get their new name right so there was an element of attention in it, loved to correct staff and disrupt a lesson and then those same students would call the same sex attracted girl in the corner a 'Dyke' which I could never quite work out - I sanctioned them obviously.
The worst case I had was two students both had incredibly complex pasts, unmet emotional and MH needs, and really needed some significant input. Instead the school went along with it with the 'Trans' sticking plaster letting the students change their name frequently not giving them the strong boundaries both desperately needed to feel safe and secure from a tumultuous past and homelife and generally not giving them the actual help they needed.
Just be aware that self harmers also tend to go hand in hand with these children and it's incredibly common amongst that group, many of them seeing it as normal due to them talking about it with each other or online.