When we were researching psychiatrists after getting an anxiety diagnosis, some of the psychiatrists wanted to do an evaluation themselves. It would only be slightly cheaper if we had a neuropsych within the past year.
So in answer to your question, I don't think you need a neuropsych to get a diagnosis/meds for ADHD, but you may have to pay a couple thousand for the psychiatrist to do their evaluation, especially if they don't take insurance.
Some recommendations we got for our kid with anxiety (so not all of these will necessarily specialize in ADHD)
Dr. Jennifer Costello - psychiatrist, we work with her virtually and love her, she takes insurance
Dr Morse or Dr. Marcou at the Chesapeake Center -- Dr. Morse is a psychiatrist and Dr. Marcou is a developmental pediatrician, they don't take insurance, I believe they specialize in ADHD
Dr. Michelle Seelman - doesn't take insurance