Here is an example:
Based on this you would get that I like cats, hoodies, bright lights, stars, and globes.......that is if you read into it. To set the record straight I do like all those things. The one thing that these portraits don't do justice to are the eyes, personally I think the eyes are the most expressive part of any photograph, or portrait, they show a lot more of the story than is captured in the image, and as humans I think we are instinctively tuned in to read peoples eyes.
So can identity be constructed through photography? Absolutely, but not in a single image, since that is only a snapshot of someones identity.