Yes, I told my parents I had Asperger's right after being diagnosed as an adult. In fact, they knew beforehand I suspected I had Asperger's. As the OP suggested the telling of parents was a dilemma---it was not a dilemma for me. In fact, I have also told fellow workers and acquaintances when the proper moments come about. And I also tell people I have Asperger's that attend my dulcimer ministry concerts.
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"My journey has just begun."