You can check it in blockchain. Thats the worst par to bitcoin now a days that you can see anything for a certain wallet.
The openness of the blockchain is part of the reason it was created, to be an open ledger instead of having to rely on banks to keep track of transactions. If you don't want to use the blockchain then you could always stick with the bank system of closed ledgers. The PKI system was used so that names weren't attached to a wallet, unless you publish that information somewhere that someone could find.