We really need to see your workbook to help. From that screenshot, I have no idea what the Geoname column is supposed to be. You have both County and State, and Tableau is not going to recognize that correctly. You need to split that field into two separate fields. Looking at your first screenshot, NOTHING in Alabama is being recognized - that's why.
There are likely other things you need to do as well but we can't tell without the workbook (twbx format).
I just mapped your FIPS codes and get this:
Some FIPS codes start with 0 and those zeros have, somehow, been removed from your data. My guess is that you, at some point, brought this data into Excel and Excel saw them as numbers and removed the zeros. But we can use a calculated field to correct that.
// Add leading zeros where missing IF LEN(STR([Fips]))=4 THEN "0" + STR([Fips]) ELSE STR([Fips]) END
Change this new field's geographic role to "County" then you'll get this:
workbook_for_question.twbx 199.0 KB