Hmmm. A tricky question.
From the perspective of an average health insurance policy (with its standard trans-related healthcare exclusions), I would think it's always advisable to classify your conditions and treatments as relating to something other than GID. My own therapist treats me for "anxiety", and my endo treats me for "alopecia" or something like that. Covers therapy and all medication except the estrogen patches, which I buy generic and without going through insurance.
With a trans-friendly insurance policy like yours (although we don't know the full details, but congrats for getting that awesome coverage!), there seems to be no reason to hide provided you know exactly what is covered and what isn't covered. But is there any reason to be open about it? Would being open really have any advantages? Maybe - I'm sure they'd want to see a diagnosis before they start approving surgeries and suchlike, but if it's just medication and counseling that you're receiving at present, why not just keep it hidden?
It's going to take us a looooong time to start to trust health insurance companies when they tell us that trans-related care is covered. To me, it screams "papertrail!", and it might just take a minor shift in power in the next election to ensure that health insurance companies find it economically or politically unfavorable to continue offering trans-related healthcare, to ramp up your premiums, exclude treatment that would otherwise have been covered, or kick you out of the pool.
Why risk it? Like with anything to do with being trans, we should be careful who we trust with our information.
Dying to hear the details of the coverage though...