So there's some MH stuff I share with my family or well have been forced to share out of like I had no control (i.e. depression, anxiety that sorta stuff when i was younger). But I have autonomy now over my mental health now and there is some MH diagnosis that I choose not to share due to stigma. Because I know it will only impact my relationship with my family and the way they treat/understand me (they both work in health, one in mental health too lol and they have openly spoken badly about ppl with my diagnosis in the past).
My psych actually encouraged me not to share these certain diagnoses with like institutions or like my school or work or GPs because of that same stigma, like telling them wont really get me better care or treatment but could in fact hinder it. I also think my family could like invalidate my diagnosis and say because they don't think i have it, i must not (I get this a lot from friends who are like but you don't seem like you have "XYZ") and I know they think its a compliment but my god does it suck.
I guess this doesn't fit your question, but I wanted to share and say that you don't have to always tell your family if it doesn't serve what u need or want. I know many people don't get this choice though.