It's not in Peter's nature to tell secrets. There are three major occassions where Peter has voluntarily admitted his identity:
-- To Timothy Harrison in "The Kid Who Collects Spider-Man"
-- To the Press in "Civil War".
-- To Jameson in "My Dinner with Jonah".
Most other times people found the identity or came across it by accident including MJ herself.
He's a fairly passive guy in that respect.
Wow two people in the same age group talking to each other once they are living together. Obviously such a thing is a totally alien situation that can never happen.Suddenly, May's chatting up with the other Avengers and Stark's butler.