Employers rarely find out about a chapter 7 filing. One exception to this rule would be if you were being garnished by a creditor, notice of the the bankruptcy would have to be sent to your payroll department in order to stop the garnishment from continuing. The reality is that your payroll department is likely to regard your filing as good news as they will no longer have to deal with the demands of the garnishing creditor.
If you file a Chapter 13 in Washington or Oregon, your employer or your payroll department is almost always going to find out about your case. This is so because, except under extremely dire circumstances, the court is going to require your plan payment to be paid through a wage order which is submitted to your payroll department. While exceptions are made to this rule, embaressment is not one of them.