Regarding Private Key Good day. Can you help me out regarding my question.

The company (legal entity) at the moment want to confirm the fact, tha certain BTC core wallet actually belongs to her. Though, i would like to clarify: can we refer to our Private key as to prove of ownership on wallet and on it's funds?
The second option proposed by Willtech above would work well. Simply sign a message using that private key and that will prove that you are in possession of the private key corresponding to that public key. As mentioned in the answer it doesn't ensure uniqueness of the actual key, but it does prove that at the time of signing the message that you are in control of the key.