Oh. So we can go about changing your DNA all day long and you'll still be you?
No, but a ring species is an example of one species becoming another, right now, while we are watching.
"Genetic change within a population is not the same as one species becoming a different species."
From a science textbook.
"In fact, evolution can be precisely defined as any change in the frequency of alleles within a gene pool from one generation to the next."
- Helena Curtis and N. Sue Barnes, Biology, 5th ed. 1989 Worth Publishers, p.974
This is a fact. The theory of evolution is what covers how this happens and how it can create new species to explain the huge variations of life that exist.
Like when My cat got caught by a tom, her kittins were all kinds of different looking cats, thats micro-evolution I guess.