We give Johann thyroxine. A lot of people on here use soloxine (brand name), but we've had no issues with the generic versions (thyroxine or levothyroxine).
It's not a medication in the same sense as a pain medication/anxiety med/etc, but replacing a naturally occurring substance that he's lacking. Try to think of it as replacing a chemical that his body isn't making (similar to using insulin for diabetes) enough of instead of "medicating" him. I'm sure you can find a "thryoid supporting" supplement or diet plan, but it still won't replace the T4 that his body isn't making enough of. They may help to preserve what thyroid function he does have.
Good luck to Duke. I bet he will be feeling a lot better once he starts on medication.
Johann was like a different dog once we started his thyroxine.....in a good way. Back to being bouncy, happy, and healthy again. And, having hypothyroidism can lead to all sorts of long term health issues like cardiac arrhythmias......so please follow your vet's advice on meds.