Who Are We?/ First Class Analysis

I am of the opinion, and strongly so, that we are the things which we can not change about ourselves. I can change my name, so that can't possibly define me as a human being. I can change my parents ( e.g. adoption) therefore that also can't define me. I can change friends/ peers very easily, therefore they are also useless in defining who I am. I can not change the country where I was born, and it is common from an individual to be raised in the country in which they were born (although possible for a movement to happen). The location, and more importantly, the general accepted paradigm of the area can be very useful in determining a person's identity. (e.g. I have a immense sense of Lithuanian nationalistic pride, resulting from my immersion in the culture) I can not change my genetics. To an extent I am nothing but a series of chemical reactions occurring in my brain. (e.g. Should my family have a genetic predisposition to alcoholism or another disease, this may effect myself or the view I hold of myself). 

A counter argument exists to this, however. The Theseus Paradox tells the story of Theseus's ship. It was pondered that how many things on a ship can you replace until it is no longer the same ship? The same principle was applied to George Washington's ax. If the ax had its head replaced twice, and the handle replaced three times, is it still the same ax? How many things can I change about myself before I am no longer the same person? Can it be as drastic as changing my name and moving across the world, or can it be as simple as getting my hair cut?