Can a pen name protect a writer's privacy?

Perhaps, but it is not as easy as you think. The first challenge will be to keep your real name from the literary agent (and without an agent, forget about selling to a major publisher).

Example:

Your name is George E. Gardner. Your chosen pen name will be Susan Simpson. When you get an agent you will have to sign a contract. The agent will assume the name you give her is your true name but do not do that. Instead, you give her "Robert L. Anderson." (Reason: She will pass the Anderson name on to the publisher, along with your pen name of Susan Simpson, regardless of your instructions to keep your true name private.)

The contract and the copyright

Use a New Mexico limited liability company with a ghost address for your copyright. This LLC name will show up on the reverse side of the title page of your book. However, do not let the agent send you royalty checks in the name of the LLC. Instead, have them sent to your wife (if you are married), or to G.E. Gardner, "the owner of the LLC. " Use the correct SSN, which you will need to give the agent.

Result:

Even though the agent now has a correct SSN and thus all will be well with the IRS, she will have given the publisher both your pen name and what she THINKS is your true name. Although checks will go to "G.E. Gardner" at some faraway ghost address, there will be no clue that this person is anyone other than the owner of the NM LLC.