Get data set from SQLLite and populate in Spinner

I want read out the customers from db and populating them in a Spinner. The code below makes no errors, but I want that customers with the same First and Lastname should be shown only one time in the spinner, not twice. That's not working, how can I do that?

DBHelper

public String[] getCustomerList() {

            String query = "Select * FROM " + CUSTOMER;
            SQLiteDatabase db = this.getWritableDatabase();

            ArrayList<String> cusList = new ArrayList<String>();

            Cursor cursor = db.rawQuery(query, null);
            if (cursor.moveToFirst()) {
                do {
                    cusList.add(cursor.getString(cursor.getColumnIndex(COLUMN_FIRSTNAME)) + " "
                            + cursor.getString(cursor.getColumnIndex(COLUMN_SECONDNAME)));
                }
                while (cursor.moveToNext());
            }
            String[] result = cusList.toArray(new String[cusList.size()]);
            Arrays.sort(result);

            return result;
        }

Method getCustomerList()

private String[] getCustomerList() {
    String[] customerList;        
    customerList= dbHelper.getcustomerList();

filling ArrayAdapter..

 adapterCar = new ArrayAdapter<String>(this,
                android.R.layout.simple_spinner_item, getCustomerList());