Browser makers know very well that they mainly trick unsuspecting users with private mode. Chrome displays an icon with a slouch hat and officer glasses, Firefox uses a mask logo, and the slightly more conservative Edge uses a darkened browser window.
At least with Chrome and Firefox, the thought is obvious: “Here I remain unknown”. Unfortunately, private mode does not allow you to surf anonymously. Almost all browsers always describe this when a new tab is opened in private mode. But many users simply skip the explanatory text.
Private mode protects your privacy only locally on the computer. If enabled, the browser does not save visited web addresses in the history, downloads do not appear in the preview, passwords are not saved, form data is forgotten, and cookies and temporary files are deleted. Other users of the same computer cannot see the pages you have visited. But there is no question of surfing the Internet anonymously.