How does a person maintain his personality, provided that the cells of the body are regularly renewed?

The identity that needs to be saved is, in general, information. And it is just as fickle as the constantly renewing cells. All this information array is constantly replenished, changed, and the person of yesterday and today is literally two different people. Not so different that there were obvious differences, but different. Thus, the personality, one's own consciousness cannot be perceived as an unchanging constant. It exists while there are certain constant physical and informational change processes. And it ceases to exist when these processes stop. Those. constant renewal of cells, restructuring of nerve connections - these are necessary conditions for the existence of a personality. In addition, each functionally identical cell carries either information similar to its counterparts, or information recoverable with the help of neighbors.

In general, this topic is from the category of philosophical questions about Theseus' ship.

I would like to make a comparison that will not explain the essence of the phenomenon, but will become a vivid metaphor.

A person retains his personality, provided that the cells of the body are regularly renewed, just as a nation retains its identity, traditions, culture, language despite the fact that some of its representatives die.

I am not an expert and I am not in dispute with other answers, I just would like to note that neurons (nerve cells), which are associated with mental processes, were previously considered not to divide and not renew at all.

Now it turned out that in some parts of the brain, neurons are still updated. Wiki:

The dentate gyrus, along with the olfactory bulb and the cerebellum, is one of the few brain regions in which neurogenesis (the formation of new nerve cells) is possible in adult organisms [5].

So for today version - not all nerve cells are updated.

A man now and a man ten years ago are not the same thing. There is such a concept in philosophy as identity. Identity is a philosophical category that expresses equality, the sameness of an object, a phenomenon with itself, or the equality of several objects. Objects A and B are said to be identical, the same, if and only if all properties (and relations) that characterize A characterize B, and vice versa (Leibniz's law). However, since reality is constantly changing, there are no objects absolutely identical to themselves, even in their essential, basic properties. Identity is not abstract, but concrete, that is, it contains internal differences, constantly “removing” itself in the process of development, depending on these conditions. The very identification of individual objects requires their preliminary distinction from other objects; on the other hand, it is often necessary to identify different objects (for example, in order to create their classifications). This means that identity is inextricably linked to difference and is relative. Any identity of things is temporary, transient, and their development, change is absolute.

And a person does not completely retain his personality. Cells are replaced every single one for 7 years. Every 7 years you are not only a different person in terms of cells, but also in terms of consciousness. Many of your views change over such a period of time.

But consciousness is not so drastically changed. The point is, your responses are neural connections in your brain. Those actions that take place along the paths more often - leave a deeper and more distinct mark in the brain. Those that you do not often do - less often. And the neural connections fade away. Accordingly, you will not forget what you do every day, regardless of the renewal of cells in the brain. And what you did once in your life and without emotional color (on the strength of which the strength of the neural path also depends) - you will forget in a couple of days, even without cell renewal.