I tried to edit the name of the Co-borrower variable, but unfortunately, the change is not reflected. Is there a refresh cycle i.e. does it take some time for the data to get updated?

The variables in the Coborrower Profile are inherited from the Borrower Profile configuration. So in order to change the variable display name on the Coborrower Profile, you need to change the associated Borrower variable name accordingly. To do so, please navigate to Lending Setup > Variables. After this is done, you'll see the new name on both the Borrower and Co-borrower profiles.