You’re not going to get any resistance! You get to decide what name school call your child by. Documents will be done in her legal name to match birth certificate, but day to day, name she’s known as, anything that’s labelled with her name on for her (coat peg, books, etc) will be the name you choose.
You have to put down their legal name for official docs etc but most of the school forms say preferred name! And when you meet the teachers etc you don’t even have to introduce as legal name just say this is Peggy! My little brother is legally William but has always been Billy, his first day at high school they called him William on the register and he had not a clue who William was 😂😂 it then very quickly got changed to Billy (that was an admin error, my mum was very clear when she did all the forms) he’s 29 so it’s definitely far more accepted now
School should be fine, when I was at school we had a bunch of kids who didn’t use their legal names. Mostly from Nigerian cultures but that doesn’t matter.