The ship of Theseus, also known as Theseus' paradox, is a thought experiment that raises the question of whether an object which has had all its components replaced remains fundamentally the same object. The paradox is most notably recorded by Plutarch in Life of Theseus from the late 1st century. Plutarch asked whether a ship which was restored by replacing each and every one of its wooden parts remained the same ship.

The paradox had been discussed by more ancient philosophers such as Heraclitus, Socrates, and Plato prior to Plutarch's writings; and more recently by Thomas Hobbes and John Locke. There are several variants, notably "grandfather's axe". This thought experiment is "a model for the philosophers"; some say, "it remained the same," some saying, "it did not remain the same".

We don't even come close to changing all parts of ourselves like skin, face, feet, hands, etc.,

We don't even come close to changing all parts of ourselves like skin, face, feet, hands, etc., but I know that I'm not even the same person as before.

It's a great question for opening the mind, the same discussion is in very old Buddhist writings (and probably older stuff) though as a teaching point with a slightly different lilt.

As far as components - you are actually 100 trillion cells. Each one of those is a living being. In the time you have read this thousands have died and reborn. Not for one split second, EVER, were you a solid object. At no point, ever, were the same thoughts and emotions arising, just perhaps similar patterns that could be found in waves in the ocean (but only if being observed by something with the capacity to recognize it and then call it a 'pattern').

It's an ability of the human mind to abstract all of that into objects. Obviously necessary for our survival and the way we operate. It's only the mind that can conceptualize those components together as "one thing" and call it a ship, or an infinitely complex process and reduce it to a persons name. That is literally the minds job to do, so there are limitations on what dissecting this on the level of mind can do as it cannot go beyond separating/grouping/naming everything it observes. Even "mind" is a conceptualization of a phenomenon, and a truly amazing one. Something that can make you marvel at life itself instead of constantly seeing it as a project.

It's a necessary and useful ability but it is the finger pointing to the moon which has a whole other set of implications in this context. Not just semantics and mental masturbation. The deeper you see how truly "in your own head" we are, opens windows to be out of it and engaged directly with what's happening at a level and depth that makes everything before seem like child's play.