How do I deal with my employee's preferred name or gender pronoun?

The simple answer in California is to do what the employee asks.

When an employee asks to be identified by a preferred name or gender, an employer who fails to comply with this request may be liable for discrimination under the California Fair Employment and Housing Act (FEHA). An employer may use an employee’s legal name and gender (as indicated in government-issued identification) rather than the employee’s preferred name and gender only when necessary to meet a legally-mandated obligation, such as IRS documentation or reports to other government agencies.
For example, if an individual has identified as female on their their government issued ID, you can report them as female for insurance purposes, employment statistics, and EEOC reporting, However, if this same person asks you to address them with a non-female pronoun, you and the rest of your staff must comply.