Your post has really pissed me off.
As a teacher with ADHD (and also a son with ASD/ADHD), I think it's awful that you're making it out to be something to not be proud of and to be embarrassed about other people knowing and having to hide it.
I see my "disability" as a super power - I can hyper focus, and therefore do really well at certain things. Straight A grades at GCSE. And yes, I'm really annoying sometimes as I talk too much and often struggle to remain on task, but then "normal" people can be annoying too.
No, the teacher should not have discussed with her child about your son having ADHD, but the whole attitude of having to hide ADHD is even worse.
If my DD gets asked about her brother having ADHD/ASD, she just says yup, he's super clever and super annoying! We speak of it as a positive thing. As do many other people.
I also teach lots of kids with ADHD, and I embrace their talents.
Being different shouldn't be a stigma - it should be celebrated.
Just have a polite word with the teacher about your DS1 if you're not happy about what she said.