My surname is a feminine name and I do occasionally get people misreading my email address (forename.surname@etc...) in reverse, although I do always sign the email off:
Mostly, I'm fine with either correcting the person after a few emails, or calling them, or they realise in their own time. However, most of my contact with customers is in a support role, where the customer's feelings towards me personally only really affect my effectiveness as a support engineer. In other words, if they feel embarrassed at their mistake or affronted by my correction, it doesn't really change anything.
Recently, my role has shifted more towards providing sales information. Now I have a situation where a business analyst is analysing my product via email correspondence. I feel I can't easily correct the person without potentially jeopardising the sale because the person's impression of me may influence their decision and I certainly wouldn't want to make them feel uncomfortable.
Do I correct them, or wait for them to realise? Clearly if I call them, they will realise, but is it better to correct them via email so they aren't put on the spot?