My therapist has joked about potential scenarios where she would be meeting my mum (e.g. helping me move my stuff out if I found my own place - she said “she wouldn’t know who the hell I was” and laughed) but she isn’t serious and I don’t think I’d want that anyway, although I think they’d get along just fine if they did meet. It’s just all the questions I’d get that I’d rather avoid!
I agree though, that unless there’s some kind of issue going on your mum needs to know about, for some reason, new therapist doesn’t need to involve her.