I feel very mixed on this subject.
My DS has ADHD and ASD combined. His ADHD is very much the prevalent diagnosis. When people ask or I describe him to people, I often say he has ADHD and Aspergers. The reason I do this is because he really does not fit the autistic profile, as it is understand by the public or even professionals. He has great theory of mind, no obsessions, is very intelligent, no strict adherence to routine, no meltdowns, doesn't struggle with transitions. I've noticed that when I describe him as being diagnosed with ASD, people make assumptions about him and what his behaviour must be like. Not just friends and family, but professionals too. They seem to 'get' him more if I describe him as having Aspergers. After DS got his ASD diagnosis, his school started attributing autistic traits to him that he didn't have. For example, one time he was upset about something that had happened in the playground, instead of investigating why he was upset, they said it 'must be because he was struggling as mufti-day was coming up which was out of routine'. To reiterate, my DS has no problems with routine whatsoever, I could tell him we were hopping on a plane tomorrow to go to Timbuktu and he'd be excited and happy as anything. I told the school he didn't have an issue with routines, and they nodded and changed what it said in his notes. It was very obvious they were simply looking for 'Autistic traits' after my DS's diagnosis and didn't really know DS. It was at this point I thought the ASD diagnosis is somewhat problematic for my DS.
As an aside, having gone through the diagnostic process with my DS, I do feel as though I could get a diagnosis of autism, if I wanted to. It's not a physical illness where a blood test can determine whether it's 'yes' or 'no'. It's based on traits, information and the subjectivity of the psychologist (whilst yes, adhering to guidelines in the DSM-5). There are people who get diagnosis of Autism which are later changed to ADHD, SPD and vice versa.