ECDSA public key point uniqueness [duplicate]

I'm new to ECDSA and there is something I still not sure about. If I have a classic Certificate Authority server that delivers PEM certificates containing public key with ECDSA, I can retrieve the coordinates of the Point on the curve, and the curve used.

My question, is regarding the coordinates of the point $$x,y.$$ Is it possible that two different generated certs can give me the same point?

Or points are sure to be unique?

Is it safe to set ownership from the combination of $$x,y.$$ For example, I have an asset and I want to set its owner to "$$\{x\}:\{y\}$$" ?

Thank you,

Without explaining all details of ECDSA, a public key consists of a curve $$E(\mathbb{F}_p)$$ and a point $$P \in E(\mathbb{F}_p) \setminus \{0\}$$.

The point $$P$$ is a random point chosen from all points of the curve (minus the point at infinity). Because the number of points must be large to be secure, it is very unliky that two randomly generated public keys share the same point.

For example, for secp256k1 (the curve used for bitcoin) you have $$115792089237316195423570985008687907852 837564279074904382605163141518161494337 - 1$$ possible points.

Without more details of the applications, it is probably safe to use the coordinates of the point to identify peers.