I don't know about private schools, but as far as I know public schools won't have a problem with you being "known as" by another name.
I went to an AU public high school, and was known only by a name that wasn't my legal name.
All my reports, school certificate, etc were all in that name. I did leave in 2001 though - times may have changed.
I know they shouldn't have an issue with you using a preferred name (a name to call you that isn't the one on your official school records - a different situation to the above).
If it's a public school you're moving to, I'd let them know about your gender issue. They might further accommodate you by allowing you to be known as male (male uniform, maybe change in staff loo for PE, etc), male name and pronouns, and any other accommodations they can think of.
In a public school (like in all government institutions - including government jobs as I can personally attest to), they have an obligation to be politically correct and treat all students equally. That includes the trans ones

.
If it's a private school you're moving to, then I have no idea. Most of them are religious. You might get away with an androgynous "known as" name.