I am my thoughts. My thoughts are me. Intertwined for all eternity
How could you be something that you can observe? Is your hand "you" in a deeply meaningful way?(beyond mere language and convention) Can't someone cut it off? What would it be then, when it's lying there and you're looking at it? Maybe you'd still say "That's my hand" but it would lose meaning, especially with time. That can't be how "you" works, right? One second this is you, another it isn't.
"You" were also once a child, but ... right now as you reflect on yourself as a child, that doesn't feel like you? It's just a memory. It's almost like you're talking about a country you once visited.
But yeah, meditation gets very into the philosophy of personal identity. It could be useful to observe your mind if you're interested in the idea of "you". That's all meditation is, observing the mind without judgement, and with attention.
Here are some insights to get your appetite going:
Are you in your head, looking at the world outside? It's quick and easy to test, actually. Just stare at a plain wall for a few seconds in the same spot. And then try to change the spot on that wall you're staring at, into an image. You can do this with your eyes closed almost certainly. If I ask you, "close your eyes and imagine a rabbit". It could be blurry, it could go away quickly, but you're still constructing the image, right?
So now just do it on the wall with open eyes. Anything you want. I do a candle with a flame that moves. I heard some can't do this but most people can do something. And what that shows you is, what you're seeing with your open eyes is not the outside world, but is a representation from your brain. It's part of mind. That also makes sense neurologically because you can't "see" the outside world, light has to travel to your retina, and your brain has to construct an image. It's not that the image then gets played out onto reality like a projector, that image is constructed in consciousness, which is what you are. You are consciousness. That's why you can form the picture of something on the wall you can stare at. So you can conclude that "you" are not inside your head, looking at the world outside. Which is how things appear to us, only, and we take as granted, and form this idea/assumption that we're behind our face and the world is in front of us, separate from us.