When you want to compare a single variable to a list of values then the IN operator is your tool of choice:
countyname in ('Thisname' 'Thatname' 'Another name');
Subsetting the data could be done with either a Where statement or dataset option or an IF statement:
Data want;
set have;
where countyname not in ('Thisname' 'Thatname' 'Another name');
run;
or
Data want;
set have;
if countyname not in ('Thisname' 'Thatname' 'Another name');
run;
If the list you want to keep is shorter then don't use the NOT in the above examples.
The IN operator for character values is equivalent to a bunch of equals, so if you have case differences such as your values with "Name" "name" "nAme" etc, for spelling you will need to address that somehow.