Parents of children with difficulties can be roughly divided into two groups.
First, there are those who think a diagnosis 'labels' their child. They don't want their child to be defined by their difficulty and believe that if you focus on what is wrong, it will stick to the child for the rest of their life. They tend not to tell others that there is anything amiss with their child.
The other group is those parents who think a diagnosis is helpful because it defines what is wrong. They believe that if you know what is wrong, you can take steps to fix it. They think that it's not 'labelling' if it's true, and they'll talk freely about it.
I'm a parent in the second group. I have no problem whatsoever with referring to Bright Eyes as 'an ASD child' or 'mildly autistic'. In fact, I usually tell people straight off, mostly because he is now at an age where people expect him to interact normally with them. As he doesn't look odd, it's not obvious that his developmental age is much younger than his physical age, so people are often surprised by his behaviour or responses.
As well, I find it helpful to talk about his autism, just for myself. It helps me work it all out and accept it all. And I think it gives others a realistic picture of my life and the challenges I'm facing right now.
I find myself having to explain Bright Eyes to our 7 year old and her friends too. I don't usually use the words 'autistic' or 'ASD' but I do talk about him needing to learn to talk, and the fact that he thinks about things a little bit differently, so we're helping him to learn to think better.