"Identity" is a popular concept in counselling and psychology today. It more accurately ought to be called "sense of identity." It expresses the (true) principle that how people see themselves is central to how they will live. "Identity in Christ" is not so much a theological term as it is a way to express the fact that perceptions of identity indeed are important, but for the Christian they ought not to be wrapped up in family, career, accomplishments, friends, sexual orientation, or any of the other worldly things that people tend to latch onto to find a sense of identity. Rather, a Christian's identity, both the sense and the reality, is found in being in Christ.
I think most Bible teachers who talk of "identity in Christ" have in mind not just the truth of adoption and its benefits, but also the way believers ought to latch onto this truth and see themselves in a new light. This is important, biblical teaching (especially in the teen years) even if the term is not a theological one, strictly. The Puritans certainly taught the principle even though the phrase is new. And the concept comes up in classic Reformed literature like the Heidelberg Catechism's famous Q&A #1.
When I was working on a recent discipleship course for teens, we spoke often about addressing identity issues. I don't believe we ever used the word "identity" in the student lessons, but we brought up the concept. We instructed students to know and believe "who you are because you are joined to Jesus," and to live accordingly. This is how I would decribe the concept of "identity in Christ."