Search sqlite android

Sorry for my english. I try create dynamicly serch. Example: we input serch word hellow, i input h-> he is serch all word who name start in latter he-> he is serch all word who name start in latter hel-> he is serch... and so on. The word may be upper and lower case like this HeLLow. My example

   public List<Map<String, String>> getSearch(String tableName, String search) {
        String query = "SELECT * FROM " + tableName + " WHERE `name` LIKE " + search;

        Cursor cursor = db.rawQuery(query, null);
        List<Map<String, String>> list = new ArrayList<>();
        String[] names = cursor.getColumnNames();

        if(cursor.moveToFirst()) {
            do{
                Map<String, String> map = new HashMap<String, String>();
                for (int i = 0; i < names.length; i++) {
                    map.put(names[i], cursor.getString(i));
                }
                list.add(map);

            } while (cursor.moveToNext());
        }

        return list;
    }

I try do like this:

String query = "SELECT * FROM " + tableName + " WHERE name = " + search;

String query = "SELECT * FROM " + tableName + " WHERE name MATCH " + search;

its not work too, i have always list = 0