Deleting Box Folder using Box name

 You can search for a folder by name using the Search endpoint. You can limit the search results to just folders by setting the type parameter to folder. 

Once you have the folder id, you can use the Delete Folder endpoint.

Using 's example, I tested this out and it seems to work...

        BoxSearchParameters boxSearchParameters = new BoxSearchParameters("ken");  // search by name
        boxSearchParameters.setType("folder");                                     // only return folders

        BoxSearch boxSearch = new BoxSearch(userAPI);

        List parentFolderId = new ArrayList<>();
        parentFolderId.add("0"); 
        boxSearchParameters.setAncestorFolderIds(parentFolderId);

        PartialCollection results = boxSearch.searchRange(0, 10, boxSearchParameters);
        for (Iterator iterator = results.iterator(); iterator.hasNext(); ) {
            BoxItem.Info info = iterator.next();
            System.out.println(info.getName() + " [" + info.getID() + "]");
            BoxFolder boxFolder = (BoxFolder)info.getResource();
            boxFolder.delete(true);
        }