Du har brug for flere indlejrede vinduesfunktioner:
SELECT *
FROM
(
SELECT the_date, name, grp,
COUNT(*) OVER (PARTITION BY grp) AS cnt
FROM
(
SELECT the_date, name,
SUM(flag) OVER (ORDER BY the_date) AS grp
FROM
(
SELECT the_date, name,
CASE WHEN LAG(name) OVER (ORDER BY the_date) = name THEN 0 ELSE 1 END AS flag
FROM orders
WHERE
the_date BETWEEN
TO_DATE('2013-09-18',..) AND
TO_DATE('2013-09-22', ..)
) dt
) dt
) dt
WHERE cnt >= 3
ORDER BY the_date