Well, the fact that she knows you used to have a female name that had to be legally changed actually works to your advantage here. You could always say "so, I'm not sure if you figured this out by my old name, but I was born in a female body. I'm now transitioning to male because I have always felt that I am a guy and not a girl."
Or something like that. I've never had to come out while fully passing, but I have come out a LOT before because my transition was delayed and I didn't pass. I found through most of my trial and error that simple is often the best. We feel like we need to explain it all, you know? But that usually ends up confusing people more, and sometimes I found I got more support just by saying "I'm changing my sex." Lol.
Edit: it's like a friend of mine who has diabetes and sometimes needs to give herself injections at meals. She used to explain to people "ok so I'm doing this injection because..." but she found it bothered people. So now, she just whips out the needle and does it without even telling people, lol. She told me that she found if you don't make a big deal about it, neither does anyone else. I think the same thing applies to being trans. Keep it simple, and no big deal. As long as they respect your pronouns and comfort levels then I think all is well.
