There is no requirement for a notice to be published in the newspapers for most personal bankruptcies. Although bankruptcy proceedings are a matter of public record, public disclosure is usually kept to a minimum. Most people will learn of your bankruptcy only if you choose to tell them, or they conduct some specific searches.
Even if your spouse is not included in your bankruptcy, they generally must become aware of it. You will be required by the trustee to supply information during your bankruptcy regarding the income and expenses of your whole family.
Your employer will only become aware of your bankruptcy if you cannot provide detailed information regarding your earnings prior to the date of bankruptcy and the trustee is obliged to contact them for this information. Most salaried employees have the necessary information in the "Year to Date" section of their paystubs.