Explanation
No. Private or incognito mode does not, by itself, make you anonymous online. Its main purpose is to limit the browsing information retained on your device.
Mozilla says Firefox's private mode does not conceal your IP address or make your activity anonymous. Google likewise explains that websites and organizations managing your network may still observe activity in Chrome's Incognito mode.
The distinction is between local records and online visibility. Chrome removes temporary cookies and site data when the Incognito session ends, but downloaded files and saved bookmarks remain. These limits do not mean private browsing has no benefit; they mean it is not an anonymity guarantee.
Key takeaway
Private browsing reduces local browsing records. It does not make your online activity invisible.