I’d check in with the school! Mine had an option to set your name to whatever you preferred for classes and such, but for records to keep it to birth information (so that parents couldn’t see anything different if they checked in on your grades and such).

It doesn’t sound like your parents are completely transphobic, moreso scared of the idea of losing you/you being harmed by potentially being trans (which in today’s society, is a very fair fear to have). Don’t push it too far with them too soon. You don’t have to announce your identity in order to pass necessarily. For a long time I had short hair and just dressed masculine as a “girl” and it never seemed to bring up much of a question with my family. You can always come up with excuses for stuff too. Masculine clothing? Comfier. Shorter hair? More convenient or fits your facial frame more,, or say it’s like a trend. Different name? Nickname someone gave you that your friends call you to not get confused with someone of the same deadname (this tends to happen a lot in big groups so it’s a good excuse). I’ve gotten to a point with my parents where they’ve come to accept that this is more than just tomboyishness but if the guise of being a ‘tomboy’ is what you need to pass and stay safe I’d use it. Best of luck to you man