You bring up a valid point that being his emissary would paint a target on the individual, but what could you do to a being who is able to freely walk among the populous? Especially one whose power is not tied to anything. I asked mostly out of curiosity and how would other gm's rule it or how would they handle the idea? Especially considering in paranet papers it says that if you do a wikipedia search on any god; then 10 out of 10 they exist in the dresdenverse. In some shape, form or another. Your ideas are warranted and appreciated all the same as I was under the impression that the white council cannot really get between the affairs of a mortal and his patron/sponsor. Especially if the mortal in question doesn't even know who the guy even is due to his crafty and mysterious nature. Something to think and ponder on.
I think that secrecy is the way to go, here... canonically in the Dresden'verse, sometimes NOBODY knows that there's an Outsider influencing somebody. So, most of the Dresdenverse will only recognize "Emissary of... um... something big and scary and really obscure, probably from the far reaches of the Nevernever."
But Outsiders aren't ordinary "patrons" they are walking declarations of war; living, breathing death-penalties (insofar as Outsiders are "alive" or "breathe" -- but likely their Emissaries do). The White Council will not "respect" anything about that, except by respecting the danger enough not to engage until they can bring maximum overkill to the table.
Even moreso with the Winterfae. Winterfae are in a state of perpetual no-holds-barred war against Outsiders; if they think a mortal is an Emissary of one, they will do whatever they deem necessary to destroy said mortal.
So ignorance and secrecy -- nobody KNOWS whose Emissary they really are (maybe not even them). Maybe have some prior attack on them (based on someone thinking/saying they WERE outsider-linked) was put down in a manner characteristic of some ancient non-Outsider pantheon, so now the claim of "Outsider! Kill! Kill!" has been "debunked." This nicely sidesteps much of the problem.