After two beers a late Friday night, I looked at the problem again, and it seems that the solution must be to nest the query once again before the WHERE clause
SELECT * FROM (SELECT *
FROM (SELECT * FROM tbleName
ORDER BY Date_of_change DESC) as orderedTble GROUP BY Name) as finaltable
WHERE Access_level LIKE %colname%
Order BY Name
gives me the result I'm trying to accomplish.
Thanks for getting me on the right track.