Employees have the right to request referral to Occupational Health, so you might just need to be more formal/direct about it.
You also have the right to contact OH independently to consult with them.
My HR dept referred me to OH when I went back to work after a period of health problems, I had a few meetings with them where they suggested practical things people sometimes do (flexible working, new office equipment, taking breaks etc) which make up a support plan. But the plan was mine to devise, then it was signed off by my line manager, me, HR and OH.
I work for a large organisation though, so they've have very standardised procedures.
I had a formal diagnosis letter from a hospital I vaguely recall providing - perhaps that's the bit your struggling with when you say evidence of menopause symptoms?
I'm not sure I would really expect OH to be involved for menopause symptoms, but I'm far from an expert, that's just an impression I have.
I guess that would be because menopause isn't really considered a disease, as such you wouldn't get something to diagnose it and provide evidence. I think even if you did have some blood tests from the GP, some women don't get symptoms which interfere in their working life, so it wouldn't mean anything on it's own.
Perhaps what you need is to discuss it with your GP and request a sick note or something to support your OH referral? Not based on a diagnosis of menopause, but based on your symptoms which are causing you difficulties. Focusing on symptoms rather than diagnosis would be the thing. OH plans are really about how to adapt the workplace to your specific symptoms rather than diagnosing medical problems anyway.
It's inappropriate for your workplace to say you have ADHD. They're not a medical practitioner, there seems to be some blurring of lines here.