Hi,
when form is submited, what is stored is option values, those depend on how you setup dropdown, if you did
business a = 1
business b = 2
then you can change label (first part, e.g. business a) to something else and all existing record will show this new label as only values (1,2 etc) are stored in db records.
But, if you have setup your dropdown with
business a
business b
Then "business a" is used for both - value and label and if you change this all existing record that have this value will be broken, you would need to chage them manually in the database.