a friend of mine, a rabbi and a neurologist, has stopped wearing his kippah to work. he does not keep the fact that he's a rabbi a secret, not at all, but doesn't offer it up as information with patients unless he's either asked or it comes up in conversation. his reasoning (which i agree with, but want to know your opinion/the laws) is that in neurology many symptoms, side effects and outcomes of illnesses affect patients sexually. he's found that many, many patients won't even bring up these sexual issues when he wears the kippah because they feel it's inappropriate. he also doesn't want to make the patients feel uncomfortable, as many would--esp. non-jews--in discussing sexual dysfunction with an obvious rabbi. ergo, he's seen, through decades of practicing medicine, that patients, even if he brings up the issues of sex, are far less likely to discuss these problems with a man of religion. his goal is to help his patients in whatever way he can, and to make sure they feel comfortable with him as their physician.
as a non-practicing jew, raised reform, this sounds generous and shows a deep respect and commitment for helping his patients. but, again, i do not know the orthodox laws and am curious what they are in this instance.