Final answer:
The ACTH stimulation test is the next diagnostic test to confirm adrenal insufficiency after an abnormal morning serum cortisol level and symptoms suggestive of the condition.
Step-by-step explanation:
Given the low morning serum cortisol level, which is less than the screening threshold for adrenal insufficiency, along with symptoms like orthostatic changes in blood pressure, hyperpigmentation, hyponatremia, and hyperkalemia, the next recommended diagnostic test is the ACTH stimulation test. This test measures how the adrenal glands react to the adrenocorticotropic hormone (ACTH), which is produced in the pituitary gland and stimulates the adrenals to produce cortisol. An abnormal response to this test, namely a lack of cortisol production after ACTH administration, would confirm a diagnosis of adrenal insufficiency or Addison's disease.