Hello , is your last name a common name? if so this may not be a problem in the end. However ,as you are doing now ,it would be wise to address the issue prior to filing. There are several ways to do so. I am sure other members will chime in . IMO, Submit with your I-129F packet Birth certificates for both you and your fiancée. You can also submit BC's of both parents if available. I don't think your embassy is a tough one ,I may be wrong. In the end if your CO suspects you may be related as lets say cousins ,a DNA test may be asked for.
Side note: It is not illegal to marry a cousin if the state you are residing in allows it.
"Is your fiance(e) related to you?"
Check no, and be ready to show proof if requested (I don't think they will ask for it if the surname is common, but I might be wrong).
The last name is not very common I looked it up in Italy there are 46 families that have the same last name. What kind of proof would I need to show?
In your original post you stated you did research and found no evidence you two are related. I would keep all the relevant written info in this regard. As the other poster suggested, the BCs of both parents would be useful too, and the Consulate can request you to take a DNA test if doubts still arise.
I actually have no first hand experience in this matter, so hopefully someone else can chip in. Good luck!