How to ask my doctor to test me for hypopituitarism?

Just ask. Doctors are easy to talk to, if the test is indicated from your symptoms, then it may be done, ordering tests just out of curiosity is not covered by any insurances. You would have to pay for your curiosity testing.
Referral. If you feel that you have hypopituitarism discuss this with your primary care provider. If you need an endocrinologist then you can be referred.