Firstly, a diagnosis would ideally happen in childhood. But in reality, many Aspies are not diagnosed until later. Although having a parents' input is optimal, it is not necessary. In some instances, it is either not feasible or even possible, such as if the parents are dead.
Like others have posted, another close relative's input would be helpful, but it is not requisite. Do you have a trusted neighbour from your childhood? Maybe a favourite teacher? If not, then your diagnostician merely works with the information you have at hand. Another option, if applicable and/or appropriate, would be to bring something tangible from your childhood: a book report, presentation or art project. Even an old report card with a teacher's written assessment.
vamla: If you do not have it, just tell your diagnostician - I'm sure they'll understand. No worries. And, Welcome to the Wrong Planet!
Heh heh........I am ambidextrous. I found an old report card and in the box where the teacher is supposed to check whether the child is ___Right Handed or ___Left Handed (X to indicate which one), my teacher just wrote, "Yes," ticking both boxes. 
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The ones who say “You can’t” and “You won’t” are probably the ones scared that you will. - Unknown