Further, I don't know about government contracts, Medicaid reimbursement, etc., but for payroll taxes (and UI rate), you could keep the same payroll tax account at CA EDD.  You do need to report a change at EDD.

Report a Change in Business Ownership, Entity Type, or Name – Select if the business has changed ownership, entity type, or business name. Provide the reason for change. Enter the former legal entity type on the “From” line, the new entity on the “To” line, the effective date for the change, and the current Employer Account Number at the top of Item A. Complete the rest of the form with the new business information.