Never enter or expose the Private Key of the paper wallet publicly or online! The legitimate owner should be able to prove ownership by signing a Bitcoin message with the appropriate Private Key as long as (s)he has a copy of it. Otherwise you can't easily prove legit ownership. Some dudes might chime in and claim it's theirs to pretend the coins for themselves.

A paper wallet usually has a Private Key and a Public Address. To search for the owner you can try to find out via the transaction history of the paper wallet's Public Address. This requires some Blockchain analysis knowledge. But at places where there's KYC involved you won't get the owner's private details as usually this is disclosed only when official entities like police or jurisdiction is asking for it.

The least you can do as effort to find the owner in my opinion is to publish the Public Address only. The Private Key must stay offline, don't even take digital pictures of it with your smartphone or camera. Pay attention to use only safe QR code apps should there be QR code encoded data on this paper wallet.

If you're not familiar with Bitcoin what makes you think it's a Bitcoin paper wallet?

Bitcoin Private Key: starts with 5... for uncompressed key or K... or L... for compressed key, followed by a bunch of upper and lower case characters and numbers

Bitcoin Public Address: starts with 1..., 3..., bc1q... or (rarely) bc1p... followed by a bunch of characters and numbers