As an employee you never completed a W-9. You completed a W-4. That is used to determine how much tax is to be withheld, and to prepare your W-2 at the end of the year. That information is not shared with anyone but the IRS, your state tax authorities, any 3rd party payroll company if your employer contracts out payroll, and any auditors or accountants that need access to complete their jobs.
Your employer might have to complete a W-9 and give it to the businesses that paid them. That will have your employer's identifying information on it. Your information will NOT be on that W-9, nor would you give those businesses any W-9s. That information is used to determine if a 1099-MISC is required, and to prepare them if needed. The W-9 information is only shared with the IRS, the state tax authorities, and any auditors or accountants that need access to complete their jobs.