Is it possible to rationally believe that certain aspects of the identity don't change, while still acknowledging the fact that we are not the same person we were an instant ago? In other words, is it possible to believe in an ever changing identity while still believing parts of us persevere?
Your question has puzzled writers for millennia; it is sometimes known as the Ship of Theseus or Theseus' Paradox. Plutarch has it thus in Vita Thesei, 22-23:
The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.
As Plutarch states, some people intuit that the ship remains the same despite incremental changes over time while others intuit that it does not remain the same.
The Ship of Theseus is an ancient thought experiment in the metaphysics of identity that continues to fascinate us as we learn ever more about the replacement rates of the cells that make up our own bodies and wonder about our own identities and that of those around us.
There are several different ways of explaining our intuitions concerning this puzzle, all of which could be described as "possible." This Wikipedia page gives an overview of them. Being Wikipedia, it should not be taken as gospel, but it is a start.
I'm not sure about the correct self-translation of the question, but I think it's about the variability of a person throughout his life. I believe that the physical Self =the Sum of the self, for a period of time from physical birth (inhalation) to (last exhalation) physical death, in a given environment, including social. As a result, the only I simply does not exist (in other words, we can not have identity), we are constantly changing both in the direction of development and in the direction of degradation...Try to answer the question: "Who am I?"...Could it be someone between yesterday and tomorrow? Maybe it's someone just now?...Maybe this someone doesn't exist? : -),...so "Who am I?"
Take the "Ship of Theseus" example given earlier one step further.
Is it rational to consider an electron to exist and travel along a trajectory, knowing that at the same time virtual particles exist?
We could assume that in every instant a new electron and positron arise from empty space, the positron annihilates with the existing electron, and the slight gap between them is the reason we now see an electron in a slightly different place.
Movement is then an emergent phenomenon of virtual particles. Is it still real? Of course it is. This is simply a case of multiple realizations. There is no reason to see one or the other view here as more real than the other, and it is perfectly rational to accommodate all the equivalent models of the same thing at once.