Yes there is an a.m. cortisol level test that should be done in the morning. Because of the interaction with Prednisone, you need to be on a very low dose of Prednisone for the test to be accurate. If you are on a higher dose of Prednisone, the test isn't so accurate. My endocrinologist said my cortisol level wouldn't be very accurate until I was on 3 mg or less and only if I was able to hold my dose for 48 hours. Most people aren't able to do that very easily.
https://www.webmd.com/a-to-z-guides/cortisol-test
There is another test to see if you adrenals are able to produce large amounts of cortisol when a person is in stressful situations. This test is called a Synacthen Test. This test is more complicated than the a.m. cortisol level test. Most doctors won't even order this test until a person is ready to taper off Prednisone. My endocrinolgist said this synachten test wasn't necessary for me when my 8 a.m. cortisol level was low. Since I was on Prednisone for 12 years, my endocrinologist expected that I would have a low cortisol level.
https://patient.info/hormones/synacthen-test