Well, I have had a related problem nearly my whole life. I have a name that is gender neutral, so people who don't know me often assume I am a man. Many times people (usually men) would write to me about some business or other and the letter would start "Dear Mr. Lee R." I find this annoying but am resigned to it. However, I hardly ever end up doing business with such people.
Then, if I do somehow exchange phone calls with the business person, it amazes me how often, even after I've talked with them by phone, that they still assume I'm a man! And there have been more than a few times when, once I meet them in person, they are shocked to see that I am a woman. And they seem to feel like I'm some kind of impersonator or have been trying to trick them. This has led to some comical job interviews.
It is really interesting to see how their excitement at possibly doing business with me evaporates once they realize that I am just some...woman. I don't bother to even take offense. It's not worth it.