Well, I haven't been testing my code. Here's a correction (also untested).
Code:
SELECT F.*
INTO KeepThese2
FROM [The Final Query] as F
INNER JOIN
(
SELECT [COLOR=red]DISTINCT[/COLOR] F.names_1
FROM [The Final Query] as F
LEFT JOIN
(
SELECT names_1
FROM [The Final Query] as F
GROUP BY names_1
HAVING COUNT(*) >=6
) as NamesToReject
ON NamesToReject.names_1 = F.names_1
WHERE NamesToReject.[COLOR=red]names_1[/COLOR] IS NULL
) as NamesToKeep
ON NamesToKeep.names_1 = F.names_1