I'm a teacher.
I think you need to get some perspective here.
There is no such thing as confidentiality in a school when it comes to any type of learning need. I've got several students in each class with ADHD, autism, dyslexia, etc - and they all need extra time or laptops or whatever whenever we do assessments, so all the kids know who the kids are with additional needs in their class as it's very much out in the open.
And guess what? No one cares. We celebrate neurodiversity week at school, we encourage students to share their experiences to raise awareness, and we actively promote the benefits of neurodiversity. It's 2025. There's no reason to be ashamed of having ADHD and quite frankly you shouldn't be teaching your child to feel this way about their diagnosis.
It's important that children understand and appreciate that everyone is different, that some people have conditions or illnesses or whatever that might make them struggle with certain things, and that we're all here to help and support each other and not judge or make fun.
With regard to this specific teacher and her child in your younger son's class, you have absolutely no knowledge of how this got passed on to her child, and so therefore complaining to the headteacher or Chair of Governors (ffs!!), claiming she has 'breached confidentiality' is a ridiculous escalation and also not necessarily the truth. Her son may have overheard her speaking to a colleague, or seen an email, or something of that nature - or she may just have accidentally said something in response to her son saying something like 'you teach my friend's brother, Jack' and her saying 'Jack who?' and him saying 'my friend says he's really naughty' and her saying 'oh he's not naughty, he's just got ADHD', and then her son saying 'what's ADHD?' and her saying 'oh, it's a type of special need.' All very innocent and unthinking.
I really wouldn't see this as something to get het up about. I'd be more concerned as to why you're so intent on treating your son's ADHD as a shameful secret.