I didn't think neuropsych testing is just for cognition.
It is essentially to test cognition.
A vague framework:
1) All psychologists are trained in administering and interpreting emotional tests and IQ tests. All training will include testing for emotional stuff like substance abuse, affective disorders.
2) Some get or choose more in depth training in this area during their general training. Some get or choose more anatomy/physiology/etc during their general training.
3) We do 4-6 years of classwork and clinical rotations. THEN we do a year old "residency" that used the same match system as medicine. After we complete our "residency", we graduate with our degree.
3) AFTER graduating from "residency", some psychologists do an additional 2 year fellowship in neuropsych. This encompasses anatomy/patho/phys/etc. The general idea of neuropsych is to differentiate psych complaints from neuro complaints OR to measure cognition for a specific purpose (e.g., a Kiloh-esque pseudodementia vs Alz). Just like in medicine, some residencies have reputations in different areas (e.g., epilepsy, gero, TBI, etc). In doing a differential like pseudodementia vs dementia, the neuropsychs are probably somewhat better at some emotional testing than some psychologists, but not all. The aforementioned might be similar to the skills of a psychiatrist vs. a pathologist in reading labs, I dunno.
4) In practice, neuropsychs are generally seeing people for specific cognitive complaints or specific neuropathologies (e.g., patient complains of memory loss, OR obtain baseline for patient who has recently been diagnosed with Parkinson's OR differential dx between binswangers and alz). There are absolutely emotional components and complaints to all of this. In an ideal patient, the test results show it's just emotional.
So the point was that in just asking for emotional testing, you're kinda missing an additional 2 years of training. Maybe having someone that has more training suits your needs for another reason, I dunno.
Forensics is another sub-specialty with specific training requirements.
Maybe that helps, maybe you know all that, maybe I'm wrong.