When you work with a bail bondsman, you can remain anonymous if you wish. The only people who will know your name are the bail agent and the court. Your name will not appear on any public records associated with the case.
Bail information is considered public record in the State of California, meaning that anyone (not only defendants themselves) can request this info. The details can be accessed via the Public Access to Court Electronic Records (PACER) system or the Criminal Intake Section.
For example, in California, bail bond records are generally public and accessible via the Public Access to Court Electronic Records (PACER) system.