A friend once heard me describe the experience of acknowledging to my mikveh lady that I was a rabbi (and my relief when she was not disapproving), and called it coming out. I'd never heard the term applied to anything other than telling someone about your sexual preferences before, but I'll take the broadening of the term.
The week before my wedding, I had a similar sort of experience with a mikveh lady- except that I botched it. The particular mikveh lady who "did kallahs" (and was really very lovely, helpful, and everything you want a mikvah lady to be) in my hometown offered an hour-long shmooze sometime before the actual immersion. During that time, while she was trying to inspire me about mikveh and offered me a chance to talk about last-minute questions and worries, I brought up that I would like to have a shmatta for my bracha- although I knew that customarily, brides didn't use one (contradicting my sense that such a covering is more kippah-like than marriage-linked, as I suggested in this previous post.)
I explained that I had grown up in a non-Orthodox community, and that women frequently covered their heads for prayer, and that, because of that, I didn't feel comfortable without covering my head when making blessings. I didn't say that I was still "not Orthodox". She saw that I came there with a small kerchief on my head, but I don't know what assumptions she made. Something about it left me feeling a little bit dishonest, for all that I never quite lied- I just didn't tell all the truth.
It was a sort of obscuring of my identity that I could rarely do- and never when I wore an actual kippah. Sometimes I longed for such a way to hide, when I didn't feel like explaining myself. Now, I blend in as Orthodox all too easily. Maybe that's why I now feel as if I oughtn't do so. And yet, there's such a desire to hide...