Here's the thing. Aside from your own bff's wishes (and yes, unlike most others on this thread, I get that she's your best friend and not your GIRLFRIEND), you also have to realize that most of the people you meet do not have the same empathy for the transgendered psyche as you do, or as your friend does even. Furthermore, you may have to consider that while you may be very passable, and your pictures suggest that you are, people who have met you for any considerable amount of time as Alex will probably read you as Lexi, even if not right away.
While you may insist on hoping that people see Lexi and Alex as two different people, you also have to understand that it's asking a lot of people who are less initiated to this world than you, to not only accept you for how you dress, but also jump through the mental hoops that you're setting up for them to treat you differently.
Furthermore, she isn't outing you to everyone she meets without your consent. If you're choosing to be in a situation where someone who knows Alex meets you as Lexi, you're choosing for there to be the strong possibility that you'll be read by them.
Now, if the preference is for you to have people refer to you as Alex in boy mode and Lexi in girl mode, that can be expressed in a way that is less mentally trying for everyone, even if means letting go of the outward concept that you're two different people.
