Use a broker to hide your identity. Brokers can buy and sell on your behalf without disclosing information about you
Use a lawyer to hide your identity. Same as a broker but protects your identity from frivolous subpoenas
Use an escrow company that supports private transactions. You can do this with Escrow.com but you need two accounts, or have a broker set up the private transaction for you using their account and your account. The escrow account creating the escrow transaction decides whether the buyer and seller can see each other's information
Use an escrow company that supports aliases. You can do this with Escrow.com by choosing a different "Display Name"