In Groosham Grange they found out that kids who joined the school were given new names, but in the sequel they still had their own names. And there were a few other things I didn't think made sense but I can't remember them right now.
they get witch names, like my 'wiccan' name is Rainbowstar, but those are only used while performing rituals. they still had to sign their original names in blood and when they go outside it's their original names that's used by friends and relatives(remember how david froze his parents during summer break lol....and then compare it to harry potter blowing up his aunt

...anyways), so i guess whether or not they use their new names when talking amongst themselves is their own choice. In fact in the real occult, you're only allowed to use your witch name during rituals, if you use it in every day use it diminishes it's power, or u'd have to be really powerful then it wouldn't make a difference.
it's a common thing that happens in fantasy books as well. you have a "usename" and then when you come of age, you get your 'real' name. but you still keep using your "usename" because if anyone knows your 'real' name it means they can have power over you
Edit(3rd of march): I just reread the book in my bath(I do most of my reading there, lol). No matter how many ti;es I read it, it is always a masterpiece

And in rereading it now I realised even more than before how big AH's influence is on my writing, expecially in the first story I ever wrote that was worth keeping(it was a vampire story, and there was a mirror but no reflection of the vampire which the main character didn't realise at first but later she figured it out....I really should never publish that story, it's a plagiary lawsuit waiting to happen, lol)