Do I Tell My Physician?

I have been seeing a doctor to treat my anxiety and depression for several years. He is in my insurance network, but I highly doubt that HRT is covered. Should I come out to the doc? I want to be under medical supervision when I start HRT. I feel conflicted about it. There is a wonderful organization where I live that serves the LGBT community that helps trans persons find help, but none of their physicians accept my insurance. On the one hand, I have built a relationship with my current doctor so I don't feel like switching. On the other hand, I want to be under supervision of a physician that has experience working with trans women on HRT.

Not looking for medical advice, just wondering how others have handled this.