Being the amateur that I am, I would do one of three things...have the narrator switch names casually: 
Casually wrote:
Mary-I mean...Sue reached down to pick up the broken vase.
Have the character in the book, the one that's writing the book, refer to her as Sue and then have the narrator switch to Sue...so...something like: 
Dialogue Change wrote:
"So you're Sue now?" I said.
Mary nodded.
"Oh...that might take some getting used to, Sue." I chuckled.
Sue smiled.
Or...more of a serious approach would be to sort of put a sentence in there that states the change has been made.
Plain and Simple wrote:
So that was the secret and it had been discovered. She was not Mary, but rather, Sue. Silently, I resigned to start calling her by her real name and with that, she became Sue...
Of course...all of those examples are really just for examples, I'm sure you can write it better, but you know, hopefully I explained the ideas well enough. 
 Bethany Faith
Bethany Faith