My son was ordered to receive a mental health evaluation and it came back horribly untrue. Can he request to have another evaluation done by a different agency?

How old is he, and why was it ordered (without going into every detail)?

While of course you can file a motion for a second eval, the court does not have to accept your motion. Again, while this is your son, perhaps you are not seeing what they saw in the eval.

But again, you can also hire and pay for your own professional to do the eval if the court appointed doctors are not giving you the result you are looking for.

In the title you ask "Can I request". In the body you ask "Can He request". These are very different things and you need to give us more background before we can answer.