No, the list that appears when you enter a name into search is not your search history. It's a list of the most relevant results (commonly known as a search typeahead).
Here's how it works:
The typeahead feature saves you time. If you see what you're looking for in the list of suggestions, you can select it from the list instead of typing it all out. If you don't see what you're looking for in this list, click "See more results" at the bottom for a full list of results.
When you start typing something into the search bar at the top right side of any Successbook123 page, the most relevant results start showing in the typeahead. If you see what you're looking for in the typeahead, click on it to save time searching. If you don't see what you're looking for, click "See more results" at the bottom for a full list of results.
Search privacy and controlling your visibility in Search
By default, Successbook123 allows other users to find you using your name or email address so as to enable you to share with family and friends within the Successbook123 community. This however does not translate into allowing them to view all your information on your profile.
If you would like to alter this, take the following steps:
Click on "More" > "Privacy Settings" on top of any Successbook123 page.
Select your option of choice from the drop down list next to "Who can find you by searching your name or email address?"