Can someone find out who owns a post office box?

The simple answer is: Yes.

When you rent a post office box, whether at the USPS or a commercial provider, you are required to provide certain information about yourself. The USPS and the commercial post office box provider are required to verify that information with a picture ID.

The purpose of the verification is to ensure that, should you be conducting illegal activities from your post office box, any interested authorities can find you.

Can anyone get this information?

No, they cannot. The USPS and commercial post office box providers are not supposed to give this information to anyone who asks.

Private investigators may conduct what is known as a "post office box break" or reverse post office box search. Many post office box owners use the box to receive financial information, such as bills, checks, bank statements, etc. If an investigatory has access to credit headers, they may be able to tie a physical address to a post office box. For example, if a physical address is used for some financial information reported on a credit report and a post office box is used for other information that also shows up on a credit report, someone with access to the reports would be able to conclude that the physical address is occupied by the same person who rents the post office box. This would be a completely legal way of obtaining a physical address for a post office box owner, although it may not be 100% accurate.

Otherwise, only law enforcement officials can access information that you file when you rent a post office box by submitting a request form or presenting a subpoena. If a subpoena is presented to your post office box provider, they have to comply and supply the information.