I suppose you could write a short message and broadcast it to the blockchain, which could serve as proof in the future that you owned that private key at a certain point in time. But I don't see the practical purpose of it.

Think about it logically. If there are funds associated with that private key, and you share it with someone, any party will be able to spend those funds and there is no way to prove who initiated the transaction. In the event of a dispute, it would be your word against theirs. Even if you trust someone completely, you can't guarantee that they won't accidentally reveal your private key to someone else, or that their own security measures will be perfect. In other words, once your private key is out there, there's no way to get it back.

So, to answer your question directly: No. There's no way to maintain ownership of a private key once you share it with someone.

Why would you want to share your private key with others in the first place? Maybe you're asking the wrong questions. There might be a better way to handle your situation.