I wonder how long it takes until the whole teaching profession just collectively decides to adopt professional pseudonyms. Would make "child at same school"-situations even more awkward I guess.

My mother was my french teacher at school three times. At home she was "mom" and in class she was "madame". It was not complicated.

That being said I did once call my male first grade teacher "mom" so maybe I'm not a good example

The issue would be safeguarding.

There's no problem what name the school has you on the books for. There's no reason what they have on file/police checks is the same name presented on office doors, emails and to parents.

We do this all the time for students that can't/won't use their legal names in school for a number of reasons.

I guess it is just a matter of getting the right systems in place to manage the administrative overhead.

There are quite a few lines of work where this might not be a bad idea. E.g. also Police and government employees in general.