Unfortunately most people still do not know, private browsing, private browsing, or anonymous surfing usually do not prevent your searches from being traced online, and that includes everything you type on Google. This mode is designed to delete history information only on your device and does not help prevent the sites you visit from tracking and monitoring your behavior to create your personal profiles.
In addition, private-mode searches are typically performed using the default search engine. This means that a non-private search engine will continue to use tracking methods such as collecting your IP address and browser fingerprint.
So, really this private mode of navigation is not that private.
It is recommended that you use this mode when you are using a public or shared computer for the sole purpose of not storing any local history, cookie, or passwords.