Assumindo que o nome é único
SELECT t1.name, (SELECT COUNT(*) FROM table_1 t2 WHERE t2.score > t1.score) +1
AS rnk
FROM table_1 t1
SELECT t1.name, (SELECT COUNT(*) FROM table_1 t2 WHERE t2.score > t1.score) +1
AS rnk
FROM table_1 t1
