Chain your charindexes.
Basically, you'll want a where clause that looks like this:
WHERE
CHARINDEX( LastName, '/') > 0 -- / exists
AND CHARINDEX( LastName, '/', CHARINDEX( LastName, '/') + 1) = 0 -- No second /s
I'll avoid discussing how much the design decision there makes me cringe... it's very denormalized.
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