The name of each search is within the search tab. If you have several search tabs up then select the arrow to the right to select the next or previous set of search tabs.
To close search tabs, click on the red cross on the left of the search tab. Alternatively, control-click the search tab & choose close search.
To clear search from memory, you have that option from the search box window, here
Search box autocomplete options. Else, go to LW's preferences, View>Autocomplete & uncheck this option.