I use my American married surname on all official documents (

Unfortunately your codice fiscale won't match your married name, and therefore it will require either changing,  or getting a new codice fiscale using your married name (not really legal but much easier to do).  Italians dont change their surname on marriage, so its not an easy process.  There is a thread on here that explains how to do it.  If I can find it Ill post the link. 

You must go to an Italian consulate, if you are outside of Italy, or to a tax office in Italy - with the two passports and a declaration issued by the municipality where you were born (Apostilled with translation sworn in Italian), where it is written that you, an Italian with an Italian passport, are the same person as you, an American citizen with an American passport - and ask that one of the two tax codes be associated with the other - so that you have a tax code only - Once you have obtained this unique tax code, you can buy in Italy both as an American citizen and as an Italian citizen, but with a single tax identification -

At most, if you apply for a mortgage, you will also have to present your American tax code , according anti-money laundering italian and Usa laws