Pude resolver esto cambiando DESPUÉS por ANTES en el activador, lo que al principio creí que no funcionaría, o:
CREATE OR REPLACE FUNCTION Insert() RETURNS TRIGGER AS $ReplInsert$
BEGIN
IF (TG_OP = 'DELETE') THEN
INSERT INTO "log" ("Operation","ID","NAME")
VALUES ('DELETE', OLD.ID, OLD.NAME);
RETURN OLD;
ELSIF (TG_OP = 'UPDATE') THEN
INSERT INTO "log" ("Operation","ID","NAME")
VALUES ('UPDATE', NEW.ID ,NEW.NAME);
RETURN NEW;
ELSIF (TG_OP = 'INSERT') THEN
INSERT INTO "log" ("Operation","ID","NAME")
VALUES ('UPDATE', NEW.ID , NEW.NAME);
RETURN NEW;
END IF;
RETURN NULL;
END;
$ReplInsert$ LANGUAGE plpgsql;
CREATE TRIGGER logTrg
BEFORE INSERT OR UPDATE OR DELETE ON "FIRST_NAME"
FOR EACH ROW EXECUTE PROCEDURE Insert();