Currently when you see the list of items in ArcGIS online open data it defaults to showing the data by relevance. We would like the default to be by name but I believe this functionality is currently not available as a configurable option or through customizing the HTML code. In the Site Editor, the search bar is not an item in the Site Header or the Body Content. This is the default setting that resides in the back-end of ArcGIS Open Data.