The letter translates (through Google Translate) as this:
In reference to your request on the extract of the birth of Mr. Dominic Barber, it announced that, following investigations show that the date of 28.10.1886 was born in Catona and Mr. Francesco Barberi Nunziato, Barberi son of Nunzio and Maria Romeo as a certificate attached. Remain available for further clarifications, send regards.
The problem here is that my great grandfather's name is Dominico, not Francesco. Everything else is exactly correct though; his birthdate, mother's & father's names, and the Frazione where he was born.
I guess I need to know first what I can actually use an extract of the birth certificate for. Second, how do I approach the wrong name situation?