Yup, and obviously having a redirect from Trentino to the Province of Trento, and Trentino bold in the body of the article takes care of any other unlikely confusion.  Give some credit to our readers.    It is the same situation as was done with Bolzano-Bozen.  Also, in English we call this province Alto Adige or South Tyrol.  Both are commonly used.   Regularly BBC will interchange terms.