Interpreting Kierkegaard is made problematic by Kierkegaard's strategic use of a pseudonyms as a rhetorical strategy. The book under consideration here, The Sickness Unto Death, was written by Anti-Climacus. Unsurprisingly, Anti-Climacus can be contrasted with Johannes Climacus. Johannes Climacus's main work is Philosophical Fragments. So if we're reading Kierkegaard, we need to be poised to understand what the rhetorical position Kierkegaard is setting for himself is. Climacus is kind of a wild thinker, concerned only with the subjective appropriation of knowledge and convinced that the rational path of the philosophers through inference cannot obtain to the important matters. By contrast we see Anti-Climacus working things through like a good dialectical and properly metaphysical philosopher in the Sickness unto Death.
This brings us to the first real point: namely, what Kierkegaard means by "being a self" in Sickness Unto Death is attended by a strict metaphysical interpretation of the self. To simplify matters greatly, there are several different ways of "not being oneself", all of which with their own dialectical structure. These deficient modes of subjectivity arise from the nature of subjectivity itself to be tasked with synthesizing the metaphysical polarities that Kierkegaard prizes: infinite/finite; eternal/temporal; totality/partiality; universal/particular. To not be oneself means: to not have synthesized these opposites properly. You thus must avoid reading the word 'self' in Anti-Climacus's writings as having the ordinary meaning that we use it in everyday language or even in present-day psychology.
Finally, to speak directly to your question:
What I got is that Kierkegaard sees want to change as an attempt to get rid of myself and be another self either if I win for eg and became and an emperor or if i failed i would be abandoning my true self ..does this means that he sees any change i make ,any improvement to my personality as an attempt to be someone else ?is true self synonymous to no change at all ? I am sure I am missing something because How would people improve then ?
In short, you're making too light a matter of what it would be to "get rid of myself and be another self." Going from being a pauper to an emperor is not getting a new self, for Kierkegaard, since it hasn't anything to do with the synthesis of the eternal and the temporal. In my view, the book you're reading from is making pretty light and loose use of Kierkegaard here for the sake of some rhetorical goal. This is amplified by the defanged, sterilized, and secularized account of the solution Kierkegaard provides, which is a misrepresentation bordering on fraud. Kierkegaard pretty literally says you have to rest in a higher power in the final sections of Sickness Unto Death. Just as there are an uncountably infinite number of wrong answers to a math problem, and only one correct one, there many different ways to fail to be yourself; only one way to be yourself. Your authors fail to mention that the "courage to be oneself" means the courage to rest in God; it is like throwing oneself down a bottomless pit and resting in the eternal free-fall. This makes him way more radical than any of the other existentialists, in my opinion, most of whom would abhor the suggestion.