I suppose it'll happen that lay people won't believe you have ADHD if you don't seem hyperactive. I gather the most you need in that respect is an active mind.
ADHD is a controversial ailment, though its existence (or the existence of something very like it) isn't often doubted.
https://en.wikipedia.org/wiki/Attention ... troversies
One thing I agree with is that there are definitely people who can't (rather than won't) pay attention under certain circumstances. I'm one of them. The unfortunate thing is that it's invisible to others, so it's natural that they could be suspicious. Society is rather competitive and the last thing competitors want is for individuals to be able to have invisible disabilities accepted and adjustments made. Much like ASD. It seems that the only acceptable proof is a note from the Great and Good for many people, and even then, they may dismiss it as psychobabble.
Frankly I don't usually tell people that I have trouble with my attention. In an ideal world I should, and I do if the person is likely to believe me, but otherwise I just hide it as best I can. It sucks.