How do I remove search suggestions from iOS Safari?
Those entries appearing as completion suggestions in the mobile Safari drop down under "Google Search" (or your default search engine of choice) are locally cached and are from your personal search history: e.g. somebody on that icloud account had typed "stranger things" in before -- not necessarily on that specific browser.

It can be cleared in the Settings > Safari > Clear History and Browsing Data. This will clear history, cookies, and cached pages (but not bookmarks or passwords) from the browser and from linked iCloud browsers. I tested this, and suggestions disappeared from my Safari "Google Search" list.

Unfortunately there does not appear to be a way to delete cached searches without deleting cached pages.

For a walk through see for example: Cult of Mac: Clear Your Browsing History And Web Data From Mobile Safari -- iOS Tips