What is the nature of the two hemispheres of the brain? What are WE?

[Yourself]

14 hours ago, Souper said:

But then, how do people who DO have identical twins differentiate themselves using DNA?

Well, humans don't develop in isolation.  DNA is mostly just a starting point, from there every interaction with the environment (which means every moment of your existence) influences what you become.

To drive this point home in a rather not subtle way: one identical twin could lose a limb in a tragic and amazingly unexpected cake decorating accident.  The loss of that arm is clearly not defined by that twin's DNA, but it will certainly become part of their identity then on.

Of course nothing so drastic is required to establish a difference between identical individuals.  DNA doesn't work by itself, it needs a whole bunch of machinery and environmental support to actually develop a multi-cellular organism and all sorts of little differences can get amplified over time.