I'm sure that once you've got over your initial surprise you will treat her the same as any other client. As others have said, we get worried by what we don't know about, but as someone who would never want to be like a racist person, i'm sure you'll not worry about it once you've got over the initial mental re-adjustment.
I have several trans-women friends and i'm sure that you understand that if you did allow your surprise to tip over and you refused to treat them because of their transexuality, you would be just as bad as those racists.
But i'm sure you won't do that.
Tips: Don't ask her what her previous name was - most trans people hate that.
You can just say that it's all a bit new to you, and hopefully you won't say anything silly or the wrong thing - and ask her if there is anything that it would be good for you to know or if she has any advice for you, and she will probably indicate if she wants to tell you more or not.
A lot of trans-people do not like people probing and asking intimate questions - but some won't mind at all, so play it by ear. If you have any more queries, you can pm me.