GROUP BY ожидает те поля, которые указаны в SELECT, кроме участвующих в аггрегатных функциях.
SELECT "workers"."name" as "name", SUM("work"."cash") as "pay"
FROM "workers", "work"
WHERE "workers"."id" = "work"."idworker"
GROUP BY "workers"."name"
SELECT "workers"."id", "workers"."name" as "name", SUM("work"."cash") as "pay"
FROM "workers", "work"
WHERE "workers"."id" = "work"."idworker"
GROUP BY "workers"."id", "workers"."name"