Dumbartonshire is a name sometimes used for the former Scottish county of
Dunbartonshire.
This is understandable, because the county town of Dunbartonshire was Dumbarton, and logic would seem to dictate that the county be called Dumbartonshire. As in many other examples of the English language, logic does not apply here, although it would be plausible for the town and county to have used the same form of the name at some point in the more remote past.