Legally, her school cannot call her by another name unless you give permission.
This is totally wrong. The school will assess the situation and, if deemed in the best interests of your child, will call them by their chosen name.
Do you know the suicide rate is now 40% every year in transgender youth? Do you want him to commit suicide?
This is both false, and a fucking awful thing to say to someone who has a child who is struggling.
I've been (still am) where you are op. It isn't easy.
My honest advice right now is support the small stuff, name, hair, clothes, pronouns, can all be changed back. If you can't use male pronouns, then please at least make an effort to use neutral terms.
If its a phase, and it quite probably is a phase, then your child still needs support to navigate through it, and they are more likely to take your advice on board if they don't consider you to be 'transphobic'.
I would also recommend getting a counsellor who is a lesbian.
My child made a lot of progress with having a gay counsellor.
It is easier to tackle the bigger issues if you seem to be on board with the smaller issues ime.
It really isn't an easy situation. My child has been on this path a long time. There has been no medical intervention, but now they are an adult they are going to transition. They have felt this was since being tiny (before trans was the thing it is now) and there were no resources or support when we started down this road.
I have made sure to sit down with my child regularly and discuss all the negatives, we have watched the ops, detransitioners stories, read about side effects and ops gone wrong, and every awful thing you could possibly imagine. My child feels this way so strongly that they are aware of every risk, and they are willing to take them. Someone who maybe isn't so strongly dysphoric probably wouldn't feel that way after going through the negatives, so I would also recommend doing that over the course of the next few months as well.
For now though I would absolutely support the small things that can be changed, your child will be more open with you if you're being supportive (even if you're faking it to an extent) and less likely to seek help and support online where there are some less than savoury people who don't have good motives.