It's not a matter of if we will ask this question, or even a matter of when. The human "I" is elusive, even to itself. It emerges from biology and will power and history and hope. The "I" that has a brain is more than the brain and more than heart and more even than its presence in this time and this place. Uniquely, it seems, "I" is what asks the question "Who am I?"
No one can fully find an answer to the question. No one system or philosophy will provide the whole of the map we need to move towards an "I" that is elusive and possibly changing as our lives change and unfold. For long stretches of time, we manage just fine without even asking the question. It is often enough to have a sort of rough sketch of our own identities and then to act as if they were, roughly, accurate.
And then it's not. Then we are facing a situation and it finally matters that "I" knows how "I" is going to respond. Sometimes these are matters of life or death. Sometimes they are matters of personal connection (who will "I" wed, bed, boss or support)? Sometimes we simply come to a crossroads with no clear reason to choose one path over another. Then we want to know: who is the "I" who will choose?
The Enneagram does not answer this question. Some enthusiasts might tell you it does, or that it is a path that leads to an answer. Everyone always hopes they have found a way to slip out of the puzzle.
What the Enneagram will do, is give you an interesting set of principles by which to approach the puzzle and an appreciation for how the puzzle is shifting.
The Enneagram suggests that you might deduce the answer to "Who am I?" by discovering patterns in how you change. What do you move towards or away from? How are you different when you are alone or in company, relaxed or under stress? How do you convince yourself or create doubt? The answer to "Who am I?" is that I am the pattern of the ways that I change.
Think about: my stable identity is a pattern of changes.