I’m an ex-lecturer. I’ve never taught children, except my own. I certainly corrected them (still do, if necessary), but wouldn’t correct anyone outside the family. I find it quite difficult not to, though.
However, I do think that people should make an effort to spell names correctly. My maiden name was very difficult to spell. I put up with years of wrong spellings, so I suppose I’m over-sensitive about it. When I was nine it was wrong on a ballet exam certificate, and that upset me very much. I felt the certificate was invalid. Bad manners have been mentioned a few times on this thread, and I think it’s bad manners not to check the spelling of names.